Question

suppose a parabola has an axis of symmetry at x = -8, a maximum height of 2, and passes through the point (-7, -1). Write the equation of the parabola in vertex form

Answer 1

Answer:

           f(x) = - 3(x + 8)² + 2

Step-by-step explanation:

f(x) = a(x - h)² + k   - the vertex form of the quadratic function with vertex    (h, k)

the axis of symmetry at x = -8 means h = -8

the maximum height of 2 means  k = 2

So:

f(x) = a(x - (-8))² + 2

f(x) = a(x + 8)² + 2   - the vertex form of the quadratic function with vertex   (-8, 2)

The parabola passing through the point (-7, -1) means that if x = -7 then        f(x) = -1

so:

    -1 = a(-7 + 8)² + 2

 -1 -2 = a(1)² + 2 -2

      -3 = a

Threfore:

The vertex form of the parabola which has an axis of symmetry at x = -8, a maximum height of 2, and passes through the point (-7, -1) is:

                                 f(x) = -3(x + 8)² + 2