Question

Suppose a parabola has an axis of symmetry at x equals negative eight , a maximum height of 2, and passes through the point Left parenthesis negative 7 comma negative 1 right parenthesis. Write the equation of the parabola in vertex form.
answer is y equals negative 3 left parenthesis x plus 8 right parenthesis squared plus 2
work out

Answer 1

To find the equation of the parabola in vertex form, we need to use the information given.

The vertex form of a parabola is given by the equation: y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.

Since the axis of symmetry is x = -8, the x-coordinate of the vertex is -8.

Since the maximum height of the parabola is 2, the y-coordinate of the vertex is 2.

Therefore, the vertex of the parabola is (-8, 2).

Substituting the values into the equation, we have:
y = a(x-(-8))^2 + 2

Next, we need to find the value of a.

Since the parabola passes through the point (-7, -1), we can substitute these values into the equation and solve for a.

-1 = a*(-7-(-8))^2 + 2
-1 = a*(-7+8)^2 + 2
-1 = a*1^2 + 2
-1 = a + 2
a = -1 - 2
a = -3

Finally, substituting the value of a=-3 back into the equation, we get:

y = -3(x-(-8))^2 + 2
which simplifies to:
y = -3(x+8)^2 + 2

Therefore, the equation of the parabola in vertex form is:
y = -3(x+8)^2 + 2.