Write an equation of the parabola in vertex form that passes through (13,8) and has a vertex (3,2).

Answer 1

Parabola in vertex form: y = a(x - h)² + k

Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)

y = a(x - h)² + k

y = a(x - 3)² + 2 <== with substitution (h, k) = (3, 2)

8 = a(13 - 3)² + 2 <== with substitution (x, y) = (13, 8)

8 = a(10)² + 2

100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50

Parabola in vertex form: y = a(x - h)² + k

y = (3/50)(x - 3)² + 2 (Final Answer - Parabola in vertex form)

Answer 2

Write an equation of the parabola in vertex form that passes through (13,8) and has a vertex (3,2).

Hello Lilian...

Vertex Form of a Parabola is: y = a(x-h)² + k , where (-h,k) is the vertex.

Substitute the vertex (3,2) into h and k.

y = a(x - 3)² + 2

Now, substitute the vertex (13,8) into x and y and solve for the leading coefficient a.

8 = a(13 - 3)² + 2

8 = a(10)² + 2

6 = 100a

6/100 = a

3/50 = a

Substitute a = 3/50 into y = a(x - 3)² + 2 and you are done!

y = (3/50)(x - 3)² + 2