SOLUTION: Write an equation for a quadratic function whose graph has x-intercepts of 3 and 7, and f(5)=8

Question 120926: Write an equation for a quadratic function whose graph has x-intercepts of 3 and 7, and f(5)=8
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
First, notice that x-intercepts in a quadratic function are easily identified when we set the function =0. After factoring such a function, we will get something resembling:. That equation, to be true, must have either factor =0. That is, or . Then, the x-intercepts are a and b because they satisfy each equation.
You should now be able to see that we are looking for a modified version of the following equation: . When we expand this, we get . Let the left side be our .
Then, . If we take . Then, what should we multiply -4 by to get an answer of 8? implies . Now, multiply the right side of the we found by this , to form a new function :

Check:

Note that , AND the zeros remain unchanged. For a simple graphical example, look at the following:

RELATED QUESTIONS
Find the rule of a quadratic function (in general form) whose graph has x intercepts at... (answered by josgarithmetic)

1.Write a formula for a function with a graph that has exactly two x-intercepts, one at... (answered by stanbon)

Find a formula for a quadratic function whose graph has x-intercepts at (1, 0) and (5,... (answered by josgarithmetic)

Determine a quadratic function whose graph has x-intercepts of (8,0) and... (answered by Alan3354)

Write an equation for a function with a graph that has x-intercepts at �3, 4 and... (answered by nerdybill)

Write an equation for a function with a graph that has x-intercepts at -3, 4 and... (answered by MathLover1)

Write an equation for a function with a graph that has x-intercepts at -3, 4 and... (answered by josgarithmetic)

Find the quadratic function y=f(x) whose graph has a vertex (-2,3) and passes through the (answered by Solver92311)

Write an equation for a function with a graph that has two intercepts, (-2, 0) and (3,... (answered by josgarithmetic)