Suppose a parabola has an axis of symmetry at x= -1, a maximum height of 6, and passes through the point (-2,1). write the equation of the parabola in vertex form

y = - 5(x + 1)^2 + 6

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

the x- coordinate of the vertex lies on the axis of symmetry and the maximum value is the y-coordinate of the vertex, hence

vertex = (- 1, 6 )

y = a(x + 1)² + 6

To find a substitute (- 2, 1) into the equation

1 = a + 6 ⇒ a = - 5

y = - 5(x + 1)² + 6 ← equation in vertex form

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step-by-step explanation: