SAT Math Problem (7)

Question

The function f is a quadratic function with zeros at x = 1 and x = 5. The graph of y=f(x) in the xy-plane is a parabola with a vertex at (3,-2). What is the y-intercept of this graph?

Answer 1

A quadratic function with zeros at x = 1 and x = 5 will have the form

 

f(x) = a (x - 1) (x - 5)

 

We can get a from the point (3, -2):

 

-2  = a (3 - 1) (3 - 5) = -4a

 

a = 1/2

 

f(x) = (1/2) (x - 1) (x - 5)

 

The y-intercept is where x = 0.

 

y = (1/2) (0 - 1) (0 - 5) = 5/2

 

The y-intercept is the point (0, 5/2)

 

 

Answer 2

you should realize that f(x) = a(x-1)(x-5) is the equation of a quadratic whose roots are 1 & 5.

Also, the pair (3,-2) satisfies this equation, thus enabling you to calculate x.  Then the y-intercept is f(0)=a(0-1)(0-5).

You can take it from here, I hope!