Suppose a parabola has an axis of symmetry at x = -5, a maximum height of 9, and passes through the point (-7, 1) . Write the equation of the parabola in vertex form.

Solution:

The vertex-form of the equation of a parabola is y = a(x - h)² + k

where (h, k) is the vertex point.

We are given that 9 is the maximum point, and that the axis of symmetry is the line x = -5.

The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5.

The maximum height is 9 means that the y-coordinate of the vertex is 9.

So: (h, k) = (-5, 9).

We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation.

y = a(x + 5)² + 9

1 = a(-7 + 5)² + 9 

a(-2)² = 1 - 9 = -8

4a = -8

a =-2

Therefore, y = -2(x + 5)² + 9 is the equation of the parabola in vertex form.

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Suppose a parabola has an axis of symmetry at x = -5, a maximum height of 9, and passes through the point (-7, 1) . Write the equation of the parabola in vertex form.

Summary:

Suppose a parabola has an axis of symmetry at x = -5, a maximum height of 9, and passes through the point (-7, 1) , the equation of the parabola in vertex form is y = -2(x + 5)² + 9.