Question

Someone please help me!

The vertex of the graph of a quadratic function is (3,1) and the y-intercept is (0,10). Which of the following is the equation of the function?

A) y=2x^2-12x+10
B) y= -1/2x^2+3x-11/2
C) y=x^2-6x+10
D) y=2x^2-7x+4

Answer 1

The standard form of a parabole is: (y-k) = a(x-h)², Where (h , k) are the coordinates of the vertex
In the example Vertex (3,1) ,
so (y-1) = a(x-3)². (a)
Now let's calculate a. The y-intercept coordinates(0 , 10), Replace in (a) x by 0 & y by 10:
(10-1) = a(0 - 3)²
9 = 9a and a=1
The equation becomes : y-1 = (x-3)², Expand (y-1) = x²-6x+9
and finally y = x² - 6x +10 (ANSWER C)