Consider the function.

Question

Consider the function and show your work for all questions.

f(x)=x^2 + 8x + 12

1. Find the vertex. Give an ordered pair.
2. Find the x-intercept(s), if any.
3. Find the y-intercept

Answer 1

The formula for the x coordinate of the vertex is -b/(2a) So for this problem you would get

x=-8/(2)=-4

To find the y coordinate of the vertex, plug in the x coordinate and solve

f(-4)=(-4)² + 8(-4) + 12

=16-32+12

=-4

The vertex is at (-4,-4)

For the x intercepts, set the y value equal to zero and solve.

0=x² + 8x + 12 Factor

0=(x+6)(x+2)

Which means x=-6,-2

The x intercepts are (-6,0) and (-2,0)

For the y intercept, set the x value equal to zero and solve.

f(0)=(0)² + 8(0) + 12 =12

The y intercept is (0,12)

Answer 2

If you have calculus, you know that the vertex occurs where 2x+8=0, i.e. at x=-4.

If no calculus the vertex occurs at x = -b/2a, i.e. -8/2 in this case.

The equation factors (x+2)(x+6), i.e. roots are -2 and -6.

The y intercept is y=12 (where x=0).