Question

The equation of a parabola is given in factored form.

y=-1/4 (x+ 2) (x + 10)
Which statement best describes the graph of this parabola?

Answer 1

The parabola's axis of symmetry is x = -6

Explanation:

Parabola general equation:

y = a*(x - r1)*(x - r2)

Equation given:

y = (-1/4)*(x + 2)*(x + 10)

a = -1/4

r1 = -2

r2 = -10

To check if the parabola passes through the point (2, 10) it is necessary to replace x = 2 and check the y-value, as follows:

y = (-1/4)*(2+ 2)*(2 + 10) = -12

Then, point (2, 10) is not included in the parabola.

If a > 0 then the parabola opens upward; if a < 0 then the parabola opens downward. Then, the parabola opens downward

Axis of symmetry:

h = (r1 + r2)/2

h = (-2 + -10)/2 = -6

Then, The parabola's axis of symmetry is x = -6

To find Parabola's vertex, replace with the axis of symmetry:

y = (-1/4)*(-6 + 2)*(-6 + 10) = 4

Therefore, the parabola has a vertex at (-6, 4)