Write the simplified equations of the function whose graph has a vertex of (-1,5) and contains the point (2,-4)

Answer 1

vertex (-1,5) another point on the parabola is (2,-4)

It's a likely downward opening parabola as -4 < 5

vertex = the maximum point

y= a(x+1)^2 + 5

plug in x =2, y = -4 to solve for a

-4 = a(3^2) + 5

9a = -4 -5 = -9

a = -9/9 = -1

f(x) = y = -(x+1)^2 + 5

f(x) = -(x^2 +2x +1) +5

f(x) = -x^2 -2x -1 +5

f(x) = -x^2 -2x +4

BUT it could also be a righward opening semi - parabola

x = a(y-5)^2 -1

plug in the other point (2,-4) to solve for a

2 = a(-4-5)^2 -1

2 = 81a -1

81a = 3

a = 3/81 = 1/27

x = f(y) = (1/27)(y-5)^2 -1 is another function if y is limited to values less than or equal to 5

or there's an infinite other diagonal shaped semi parabolas that have the same vertex and go through the given point.

But the answer you want is most likely the vertical parabola, the first solution above.

Answer 2

f(x) = a(x + 1)² + 5, Vertex form, learn it.

-4 = a(2 + 1)² + 5, substitution of point

Solve for a.