Question

What are the important points needed to graph `F(x)=3x^2+4x-1`?

Answer 1

`y-`intercept and its reflection, `x-`intercept(s), and the vertex.

Explanation:

There are 5 points which you can determine which will allow you to sketch the curve of the parabola. You can find....

`1.rarr` the y-intercept. This is given by the constant ,c. Here c= -1.

`2.rarr` the x-intercept(s), Make `f(x)=y=0`
Solve by factorising, completing the square or the quadratic formula.
IN this case, `x = -1.549 and x= 0.215`

`3.rarr` the axis of symmetry. `x = -b/(2a)`
This gives the x-value of the turning point. Here, `x=-2/3`

`4.rarr` the Turning point (vertex). It lies on the axis of symmetry,
In this case, find `y = f(-2/3) = -2 1/3`

`5.rarr` the mirror image of c. Every point on the parabola has a reflection in the axis of symmetry. It is the same distance from the axis of symmetry as `c` IN this case `-2/3`
The mirror image of `c` is the point `(-4/3, -1)`

graph{3x^2+4x-1 [-5, 5, -2.5, 2.5]}