Question

Objective: Quadratic Functions

State the x-intercepts of the graph of the equation. Then find the coordinates of the
vertex. The vertex and an ordered pair must be graphed on both sides of the vertex.

3. y = (x+6)(x + 1)

Answer 1

the coordinates of the vertex are (-7/2, -25/4), and we should plot this point and the x-intercepts on both sides of the vertex.

Explanation:

To find the x-intercepts, we set y = 0 and solve for x:

0 = (x+6)(x+1)

x + 6 = 0 or x + 1 = 0

x = -6 or x = -1

So the x-intercepts are (-6, 0) and (-1, 0).

To find the coordinates of the vertex, we first expand the equation:

y = x^2 + 7x + 6

Then we use the formula for the x-coordinate of the vertex, which is -b/2a:

x = -7/(2*1) = -7/2

To find the y-coordinate of the vertex, we substitute this value of x into the equation:

y = (-7/2)^2 + 7(-7/2) + 6

y = 49/4 - 49/2 + 6

y = -25/4

So the coordinates of the vertex are (-7/2, -25/4), and we should plot this point and the x-intercepts on both sides of the vertex.