topic 6 assessment

Question

A quadratic function is defined by  is defined by g(x)=(x+6)(x−4)

a) What are the X-Intercepts?

b) What is the Y-Intercept?

c) What is the Vertex?

Answer 1

Hi Kyla L.

for

g(x)=(x+6)(x−4)

The x intercepts can be found by setting each of the factors equal to zero then solving for x

g(x) = 0 =(x+6)(x-4)

To find the y intercept of

g(x)=(x+6)(x−4)

FOIL your factors to get your function into standard form ax² + bx + c

g(x) = x²-4x+6x-24 = x² + 2x - 24

Set x = 0 and solve for y

To find the vertex for

g(x)=(x+6)(x−4)

Use your FOIL of g(x)

g(x) = x² + 2x - 24

To assign the values of a, b, and c for your quadratic in the

g(x) = ax² + bx + c

In the form above, the x coordinate of the vertex is -b/2a

Plug the x coordinate of the vertex back into your function to calculate the y value of the vertex

g(x) = x² + 2x - 24

Give that a try, graph your function a Desmos.com to confirm all your point. I hope that helps

Answer 2

a) Set y to zero and solve for x.

b) Set x to zero and solve for y. Looks like -24 to me.

c) If you multiply this out, you get y= ax²+bx+c. This is a parabola. The x value of the vertex can be found

using x = -b/2a, in this case, x = -1. The y value is, y = (-1+6)(-1-4) = -25

(-1,-25)