Question

Help! I dont understand this question:
A quadratic function has a vertex at (2,5) and passes through the point (4,9).

What is the correct algorithm for finding an equation for the quadratic function?

Answer 1

A) y = a (x - 2)^2 + 5
9 = a(4-2)^2 + 5
a = 1
y = (x - 2)^2 + 5

B) y = a (x - 4)^2 + 9
5 = a(2 - 4)^2 + 9
a = -1
y = -1(x - 4)2 + 9

C) y = a (x - 5)^2 + 2
9 = a(4-5)^2 + 2
a = 7
y = 7(x - 5)2 + 2

D) y = a (x - 9)^2 + 4
5 = a(2 - 9)^2 + 4
a = 1/49
y = 1/49(x - 4)2 + 9

Answer 2

vertex form of quadratic equation :

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

where :
vertex = \((h,k)\)

Answer 3

oh ok . . . um is h: 5 and k: 9

Answer 4

Nope.

Answer 5

A quadratic function has a vertex at (2, 5)
h k

Answer 6

^^

Answer 7

h : 2
k : 5

Answer 8

plug them in the quadratic :

\(\large y = a(x-2)^2 + 5 \)

Answer 9

you still need to find the value of \(a\)

Answer 10

Just to make it clearer, to add to what @ganshie8 said,

The vertex form of a parabola is

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

where \((h,k)\) is the vertex and \((x,y)\) is one of the points that goes through its graph.

Answer 11

In this case you were given

\((h,k) = ((2,5)\) and \((x,y) = (4,9)\)

Once you've inserted both the vertex and the point into the vertex formula, finding the value of \(a\) should be effortless.

Answer 12

@ganeshie8 :)

Answer 13

Alright got it thanks :D