The quadratic function below has an axis of symmetry through x = -4; a vertex at (-4, -9) and zeroes at x = -7 and x = 0.
y = x² + 8x + 7
1) true
2) false

True

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 4, - 9), thus

y = a(x + 4)² - 9

To find a substitute the coordinates of the zero (- 7, 0) into the equation.

0 = a(- 7 + 4)² - 9, that is

0 = 9a - 9 ( add 9 to both sides )

9a = 9 ( divide both sides by 9 )

a = 1, thus

y = (x + 4)² - 9 ← expand factor using FOIL

y = x² + 8x + 16 - 9

y = x² + 8x + 7

Line M - neither

Line N - perpendicular

Line P - neither

Line Q - parallel

Step-by-step explanation:

A line that is perpendicular will aways have and opposite slope, e.g. -3/4, opposite, 4/3.

A line that is parallel will always have the exact same slope, e.g. -3/4, same, -3/4.