Question

Write an equation of the parabola in vertex form.
passes through (10,-3) and has vertex (5,7)
A.y=-2.5(x - 5)2^+ 7
B.y=-2.5(x+5)^+7
C.y=-0.4(x+ 5)2 +7
D.y=-0.4(x - 5)2 +7

Answer 1

Answer:

C.y=-0.4(x+ 5)2 +7

Answer 2

The equation of the parabola that passes through (10,-3) and has vertex (5,7) is y = -0.4(x -5)² + 7

How to determine the equation?

The vertex is given as:

Vertex, (h,k) = (5,7)

The point is given as:

(x,y) = (10,-3)

A parabola is represented as:

y = a(x -h)² + k

Substitute (h,k) = (5,7)

y = a(x -5)² + 7

Substitute (x,y) = (10,-3)

-3 = a(10 -5)² + 7

Add -7 to both sides

-10 = a(10 -5)²

This gives

-10 = 25a

Divide both sides by 25

a = -0.4

Substitute a = -0.4 in y = a(x -5)² + 7

y = -0.4(x -5)² + 7

Hence, the equation of the parabola is y = -0.4(x -5)² + 7

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