Write a quadratic function whose vertex is (7,6) whosey-intercept is 10

Question

Write a quadratic function whose vertex is (7,6) whose y-intercept is 10

Answer 1

y = a(x-7)^2 + 6

10 = a(-7)^2 + 6

4 = 49a

a = 4/49

y = (4/49)(x-7)^2 + 6 is a parabola with y intercept 10 and vertex (7,6)

but there are other parabolas fitting that description. Yet they are not functions

just quadratic relations:

x = a(y-k)^2 + h

x = a(y-6)^2 + 7

0 = a(10-6)^2 + 7

-7 = 16a

a = -7/16

x = (-7/16)(y-6)^2 + 7 is a also a parabola with vertex (7,6) with y intercept 10

both are quadratic relations. Only the first is a quadratic function. If a vertical line through the graph intersects more than once, it's not a function.

eliminate half of the parabola, upper or lower half and you have a quadratic function.

those are horizontal and vertical parabolas. you could also find diagonal or parabolas with other angles that meet the same vertex and y intercept. they would have xy terms, but that's still a quadratic function.