How do you graph y=2x^2 -5x -3?

2 Answers
Sep 20, 2015

You can easily do this by inserting values in x and plotting some points.

Explanation:

You can graph this easily by making a table of x and y values. But first, we must find the vertex (h,k).

To solve for the vertex, we'll start with this formula (h is the value of the abscissa of the vertex.):
h=-b/(2a)
h=-[(-5)]/[2(2)]
h=5/4

Now to find k (the ordinate of the vertex), we will simply plug in 5/4 to x.

y=2x^2-5x-3
y=2(5/4)^2-5(5/4)-3
y=2(25/16)-25/4-3
y=25/8-25/4-3
y=25/8-50/8-3
y=-25/8-3
y=-25/8-24/8
y=-49/8

The vertex is (5/4,-49/8).

After plotting the vertex, just plug in other values into x and graph them. Start with simple ones such as the y-intercept (set x to 0). Remember that this is a quadratic equation, so your graph must be a parabola.

graph{2x^2-5x-3 [-14.24, 14.24, -7.12, 7.12]}

Sep 20, 2015

y= (2x+1) (x-3) graph{2x^2-5x-3 [-6.07, 7.977, -6.18, 0.847]}

Explanation:

Cross factorise the quadratic equation to get the (2x+1) (x-3) equation.

Then, put:

2x+1=0
so make x the subject of the formula
x=-1/2

And then,
x-3=0
so move -3 over
x=3

So -1/2 and 3 are your x- intercepts.

To find the y- intercept you need to complete the square, making the quadratic into the form of a(x-h)^2 + k, so

  1. Factorise 2x^2 - 5x with the coefficient of 2x^2 which is 2 (because x has to have a coefficient of only 1 !)
  2. Which makes it 2(x^2 - 2.5) - 3
  3. Then 2 [ (x-1.25)^2 - 1.56 ) ] -3
    You get 1.25 from dividing 2.5 by 2. You always have to divide the number by 2. Also, you get 1.56 (rounded up to 3 s.f) from squaring 1.25. These are all rules!
  4. Then expand the brackets, so
    2(x-1.25)^2-3.12-3
  5. 2(x-1.25)^2- 6.12

So your y- intercept is 1.25. (Ignore the negative! Always change it to positive)

And your minimum point will be (1.25,-6.12).