The vertex of this parabola is at (2, -1). When the y-value is 0, the x-value is 5. What is the equation of the parabola?

Guest Feb 27, 2020

#1**0 **

A formula for a parabola is: y - k = a(x - h)^{2}

where (h, k) are the coordinates of the vertex.

Since the vertex is at (2,-1), h = 2 and k = -1.

Putting those values into the formula: y - -1 = a(x - 2)^{2} or y + 1 = a(x - 2)^{2}

To find the value of a, substitute these values: y = 0 and x = 5 into the equation.

0 + 1 = a(5 - 2)^{2}

1 = a(3)^{2}

1 = 9a

a = 1/9

The equation is: y + 1 = (1/9)(x - 2)^{2}

geno3141 Feb 27, 2020