Given the vertex of 1,5 and the x intercept of 5,0 what is the equation for the parabola

Answer 1

f (x) = a(x - h)² + k, where (h, k) is the vertex of the parabola

Using the vertex of (1,5), we can get the following

f (x) = a(x - 1)² + 5

Next, we can plug in the other point given (5,0) for (x,y) and solve for a

0 = a(5 - 1)² + 5

Simplify the parenthesis

0 = a(4)² + 5

Simplify the exponent

0=16a+5

Subtract 5 from both sides

0-5=16a+5-5

Simplify

-5=16a

Divide both sides by 16

-5/16=16a/16

Simplify

-5/16 = a

Now that we have a we can plug it into the equation for the final answer

f (x) = -5/16(x - 1)² + 5