Question

How do you use the important points to sketch the graph of `y = 2x^2 + x − 15`?

Answer 1

See explanation.

Explanation:

We can factor `2x^2+x-15=(2x-5)(x+3)`.

From this we know the `x`-intercepts are `(5/2,0)` and `(-3,0)`.

The `x`-coordinate of the vertex is located at the average of the `x`-coordinates of the intercepts, so at `x=-1/4`. The `y`-value of the vertex can be found by substitution:

`(2(-1/4)-5)(-1/4+3) = -121/8`.

So the vertex is `(-1/4, -121/8)`.

The `y`-intercept is found by substituting `x=0` to get `y=-15`, so the `y`-intercept is `(0,-15)`.

Plotting all of these points and sketching a parabola through them we get the graph we want.

graph{y=2x^2+x-15 [-16.83, 23.17, -14.96, 5.04]}