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
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.