Question

The vertex of this parabola is at (3,5). When the Y value is 6X value is negative one what is the coefficient of the squared term in the problems equation

Answer 1

We know that equation of a parabola is given by :-

y = a(x-h)² + k

Where (h,k) is the vertex of parabola and (x,y) is any point on its curve.

Given that vertex of parabola is (3,5) and one point (x,y) is (6,-1).

We can plug the given information in the equation of parabola and solve it for value of 'a' :-

-1 = a(6 - 3)² + 5

-1 = a(3)² + 5

-1 = 9a + 5

9a = -1 -5 = -6

a = $\frac{-6}{9} = \frac{-2}{3}$

a = $\frac{-2}{3}$ is the final answer.