Standard Form of the Equation

Key Questions

• How do I find the standard equation of a parabola?

  I believe you mean standard form. Standard form has another name, vertex form.

  This is a duplicate question, please read the link below as it also has an example: How do I convert the equation `f(x)=x^2+6x+5` to vertex form?

  Amory W. · 1 · Aug 22 2014
• What is the directrix of a parabola?

  The directrix of the parabola is a straight line that, together with the focus (a point), is used in one of the most common definition of parabolas.
  In fact, a parabola can be defined as *the locus of points `P` such that the distance to the focus `F` equals the distance to the directrix `d`.

  The directrix has the property of being always perpendicular to the axis of symmetry of the parabola.

  Maurizio Giaffredo · 1 · Oct 31 2015
• What is the standard form of the equation for a parabola?

  Answer:

  See the explanation section.

  Explanation:

  The term "standard form" is perhaps overused in mathematics.

  The standard form for a quadratics function (as a polynomial function) is `f(x)=ax^2+bx+c`.

  The standard for for the equation of a parabola (also called the vertex form) is like the standard form for other conic sections.

  For a parabola with vertex `(h,k)` through the points `(h+-1,k+a)`,
  (that is, it opens up or down)
  the standard form is `y = a(x-h)^2 + k`

  (If the parabola opens sideways, it includes the points `(h+a, k+-1)` and has form `x = a(y-k)^2+h`.)

  Jim H · 1 · Oct 16 2015

• How do I find the standard equation of a parabola?
• How do I find the standard equation of a parabola given 3 points?
• How do I find the focus of the parabola represented by `y=2x^2-8x+9`?
• What is the standard form of the equation for a parabola?
• In the standard form of the equation for a parabola, what is represented by `a`?
• What is the directrix of a parabola?
• How do I find the focus of the parabola with the equation `y=1/4x^2-3/2x+1/4`?
• How do you find an equation of the parabola with a vertex of (-1,2) and focus of (-1,0)?
• How do you write the polynomial `4x + x + 2` in standard form and how many terms and degree is it?
• How do you write the polynomial `1 - 2s + 5s^4` in standard form and how many terms and degree is it?
• How do you write the polynomial `-1 + 2x^2` in standard form and how many terms and degree is it?
• How do you write the polynomial `2 + 3x^3 - 2` in standard form and how many terms and degree is it?
• How do you write the polynomial `a^3(a^2 + a + 1)` in standard form and how many terms and degree is it?
• How do you write the polynomial `2/3 + s^2` in standard form and how many terms and degree is it?
• How do you know if `5x^2-3y^2-20x-36y=103` is a hyperbola, parabola, circle or ellipse?
• How do you know if `x^2-10x-y+18=0` is a hyperbola, parabola, circle or ellipse?
• How do you know if `x^2+2y^2+2x-12y+11=0` is a hyperbola, parabola, circle or ellipse?
• What are the conic sections of the following equations `x ^2 + y ^2 - 10x -2y +10= 0`?
• What are the conic sections of the following equations `4x ^2 + 4y ^2 - 60=0`?
• What are the conic sections of the following equations `16x^2 + 25y^2- 18x - 20y + 8=0`?
• For the parabola`x-3 = 1/8 (y+5)^2`, what are the coordinates of the vertex and focus and directrix?
• How do you write the equation`9x^2 - y^2 - 18x + 6y - 36 = 0` in standard form and what type of conic is it?
• How do you write `4x^2 + y^2 – 4y – 12 = 0` in standard form and why type of conic is it?
• How do you find the equation of the following conic section and identify it given: All points such that the sum of the distance to the points (3,1) and (-1,1) equals 6?
• How do you find the equation of the following conic section and identify it given: All points such that the difference of the distance to the points (2,2) and (6,2) equals 2?
• How do you find vertices, foci, directrix, axis of symmetry of `Y+2 =1/10(x-6)^2`?
• How do you write an equation of a parabola with directrix x+y=1 and focus (1,1)?
• How do you find the equation of the parabola whose focus is at (3, 3) and whose directrix is at x = 7?
• How do you find the equation of the parabola whose Focus (0,-1/4) and directrix (0,1/4)?
• How do you find the equation of the parabola vertex at the origin and the directrix at x=7?
• What is the equation for a parabola with vertex:(8,6) and focus:(3,6)?
• How do you write an equation for the parabola with focus (0,2) and directrix y=-2?
• How do you write an equation for the parabola with vertex (-1,2) and directrix x=-2?
• How do you write an equation for the parabola with Vertex at the origin, focus at ( 0, 1/11)?
• What is the 3rd term when `4f^3 + 19f + 16f^4 - 9f^2` is arranged in descending order?
• How do you write the equation of the parabola in standard form `x^2-12x-8y+20=0`?
• Write the equation of the parabola in standard form with coordinates of points corresponding to P and Q: (-2,3) and (-1,0) and Vertex: (-3,4)?
• How do you write this equation into the vertex form `f(x) = x^2+4x+6`?
• The vertex form of the equation of a parabola is `y + 10 = 3(x-1)^2` what is the standard form of the equation?
• How do you find the equation in standard form of the parabola whose focus is at (-2, 4) and whose directrix is at x = 4?
• What is the vertex of `y = 2(x - 3)^2 + 1`?
• How do you write the standard form of the equation of the parabola that has a vertex at (8,-7) and passes through the point (3,6)?
• If a and B are the roots of the equation `2x^2 - 3x + 4 = 0`, how do you form the equation with roots a+2 and B+2?
• How do you write this quadratic equation `f(x)=5-4x-x^2` in standard form?
• How do you find the equation in standard form of the parabola Focus (3,4) and a directrix y = 1?
• How do you write standard form of quadratic equation of vertex (2,3) and yint = 11?
• How do you write standard form of quadratic equation of vertex (-1,5) and yint =3?
• How do you find the standard form of the equation of the parabola with a vertex of (-1,4) and x intercepts of (-3,0) and (1,0)?
• How do you find the standard form of the equation of the parabola with a vertex of (1,0) and two points that are in the parabola are (5,3) and (5,-3)?
• How do you find the standard form of the equation of the parabola with the given characteristic and vertex at the origin and Focus: (0, −5)?
• How do you write the vertex form equation of each parabola given Vertex at origin, Focus (0, -1/32)?
• How do you write the vertex form equation of each parabola given Vertex (8, -1), y-intercept: -17?
• How do you find the standard form of the equation of the parabola with focus (7, 5) & directrix x=1?
• What is quadratic in standard form form `y+9=2(x-1)^2`?
• How do you write `y-5 = -2(x+1)^2` in intercept form?
• How do you write `y = (x+1)(x-3)` in Vertex form and Standard form?
• How do you write a quadratic equation in standard form with the given root(s) 3, 2/5?
• How do you find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3?
• How do you find the standard form of the equation of the parabola with a focus at (0, -6) and a directrix at y = 6?
• How do you write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point: Vertex: (6, 5); point: (0, -4)?
• How do you write answers in standard form for `x^2-3/4x+1/4=0`?
• How do you write a quadratic equation in standard form that has two solutions, 10 and -4 with the leading coefficient must be 1?
• How do you write the standard Form of the parabola equation given Vertex (3 , -3) Focus (3 , -9/4)?
• How do you find the vertex of a quadratic equation `y= -x^2 + 9`?
• What is the equation, in standard form, of a parabola that contains the following points (–2, 18), (0, 2), (4, 42)?
• How do you find the equation in standard form of the parabola with directrix x=5 and focus (11, -7)?
• What is the standard form of the equation of this parabola `y^2+6y+x+10=0`?
• How do you write `y = 4(x - 2)^2 - 1` in standard form?
• How do you write an equation in standard form of the parabola that has vertex (-8,-3) and passes through the point (4,717)?
• How do you write the quadratic equation in standard form `2x^2 - 3 = -6x - 2`?
• How do you write the quadratic equation in standard form `x^2 - 12 + 4x = (x - 2)^2 + 2`?
• How do you express `y=(x-2)^2+4` in standard form?
• Which term if the linear term in the equation `y=2x^2-3x+5`?
• How do you identify the vertex of the parabola defined by `y=2x^2+8x+9`?
• How do you Identify the solutions to the equation `2x^2+5x=3` when you solve by factoring?
• How do you write the equation `3y^2 - x - 12y +14 = 0` in standard form?
• How do you write the equation `y=(x-2)^2+ 6` in standard form?
• How do you write the equation `y= -2(x+1)^2+3` in standard form?
• How do you write the equation `y= (x-4)(x-2)` in standard form?
• How do you write the equation `y= 4(x + 1) (x +2)` in standard form?
• How do you write the equation `y= -3 (x-3) (x+2)` in standard form?
• How do you find the standard form of an equation with a given Vertex: (0,0) and Point on Parabola: (3,6)?
• How do you write a quadratic equation in standard form that has two solutions, 6, and -10 with the leading coefficient one?
• How do you turn a standard form to vertex form `y=x^2-1`?
• How do you turn a standard form to vertex form `y=x^2-2x+1`?
• How do you find the standard form of the equation Vertex: ( -1, 2), Focus (-1, 0) Vertex: (-2, 1), Directrix: x = 1?
• What is the value of the coefficients when the quadratic equation `y = (5x − 2)(2x + 3)` is written in standard form?
• What is the standard form equation for the parabola y=(x-4)(x-8)?
• How do you write standard form of equation of the parabola that vertex is (2,3) and graph passes through the given point (0,2)?
• How do you write standard form of equation of the parabola given `y = -2(x+4)(x+1)`?
• How do you find the equation of the quadratic function given (1,6), (3,26), (-2,21)?
• How do you use zeros to write quadratic functions in standard form x=2 or x=-1?
• How do you write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the point Vertex (-2,5); Point ( 0,9)?
• How do you find the standard form of the equation of the parabola when it has a horizontal axis and passes through (4,6)?
• What is the equation, in standard form, for a parabola with the vertex (1,2) and directrix y=-2?
• How do you find an equation in standard form of the parabola passing through the points (1,1), (-1, -3), (-3, 1)?
• How do you find the equation for a parabola if you have (3,0), (5,0) and (0, 15)?
• How do you five the standard form of the following quadratic equations and identify the constants a, b and c `3x^2 = 5 - 2x`?
• How do you five the standard form of the following quadratic equations and identify the constants a, b and c `x - 5x^2 = 10`?
• What is the standard form of equation of parabola with vertex (0,0) and directrix x=6?
• How do you use the quadratic formula to solve the equation, `x^2-x= -1`?
• How do write standard form of equation of the parabola given that vertex is (5/2, - 3/4) and graph passes through point (-2 ,4)?
• How do you write a quadratic equation in standard form with solutions 2+3i, 2-3i?
• How do you write a quadratic equation in standard form with solutions -2 and 7?
• How do you write a quadratic equation in standard form with solutions 1 and -8?
• How do you write the standard form of the equation of the parabola whose directrix is x=-1 and whose focus is at (5,-2)?
• How do you write the standard form of the equation of the parabola that has (3,4) vertex and (1,2) point?
• How do you write the standard form of the equation of the parabola that has (-1/4, 3/2) vertex and (-2,0) point?
• How do you write a standard form of a parabola with given Focus (4, 3) and Directrix y= -3?
• How do you find the vertex of `f(x)= -2x^2 + 16x +4`?
• How do you find the equation of the parabola having its focus at `( 1/2, 1/2)` and the directrix along `x - y = 1`?
• How do you write the equation in vertex form `y=x^2-6x+11`?
• How do you write the equation in vertex form `x=y^2+14y+20`?
• How do you write the equation in vertex form `y=1/2x^2+12x-8`?
• How do you write the equation in vertex form `x=3y^2+5y-9`?
• Question #e9d48
• How do you find the equation of the parabola with the given focus F(0,3) and directrix y=-5?
• How do you find the equation of the parabola with the given focus F(-2,0) and directrix x=8?
• How do you find the equation of a parabola with vertex at the origin and focus (2,0)?
• How do you find the equation of a parabola with vertex at the origin and focus (-2,0)?
• How do you find the equation of a parabola with vertex at the origin and focus (0, -3/2)?
• How do you find the equation of a parabola with vertex at the origin and focus (0, -2)?
• How do you find the equation of a parabola with vertex at the origin and directrix y=-1?
• How do you find the equation of a parabola with vertex at the origin and directrix x=3?
• How do you find the equation of a parabola with vertex at the origin and directrix x=-2?
• How to find the equation of a parabola whose focus is `(1,1)` and directrix is `x-y-3=0`?