# SAT Practice Questions: Solving Quadratic Functions

On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: *y* = *ax ^{2}* +

*bx*+

*c*or

*f*(

*x*) =

*ax*+

^{2}*bx*+

*c*. (Don’t panic; they mean the same thing.)

The following practice questions may look scary, but they simply involve a little distribution, simplifying, and plugging in of values.

## Practice questions

**Given this equation, what is the value of***a*+*b*+*c*?

*x*(2*x*+ 3) – 2(*x*– 3) =*ax*^{2}+*bx*+*c***If***a*,*b*, and*c*are integers, 6*x*^{2}+*cx*+ 6 = (*ax*+ 2)(*bx*+ 3) for all values of*x*, and 1 <*a*<*b*, what is the value of*c*?

## Answers and explanations

**The correct answer is 9.**

Distribute and simplify the expressions on the left to match the quadratic on the right:

From this, you know that*a*= 2,*b*= 1, and*c*= 6, which add up to 9.**The correct answer is 12.**

Multiply the binomials to match the quadratic, and then simplify by subtracting 6 from both sides:

Because 6*x*^{2}=*abx*^{2},*ab*= 6. And because*a*and*b*are integers and 1 <*a*<*b*, you know that*a*= 2 and*b*= 3. Now, using*cx*= (3*a*+ 2*b*)*x*, you can plug in 2 for*a*and 3 for*b*and then solve for*c*: