# SAT Practice Math Questions: Linear and Quadratic Functions

Although functions seem like a pretty abstract concept, a huge number of real-life situations can be modeled using functions. To do well on the Math section of the SAT, you definitely want to know the most common types of functions: linear and quadratic.

All linear functions have the form y = mx + b or f (x) = mx + b. In graphing terms, m represents the slope of the line being drawn, while b represents its y-intercept.

Quadratic functions, on the other hand, have the form y = *ax*^{2} + *bx* + *c* or *f* (*x*) = *ax*^{2} + *bx* + *c*. Graphically, they’re represented by a *parabola,* a shape that resembles the basic rollercoaster hump.

The following practice questions deal with both linear and quadratic functions.

## Practice questions

- If
*f*(*x*) is a linear function with a slope of 2, passing through the point (–2, –3),*f*(*x*) must also pass through the point**A.**(1, 2)**B.**(1, 3)**C.**(2, 2)**D.**(2, 3)

- If
*a*^{2}–*b*^{2}= 40 and*a*–*b*= 10, then*a*+*b*=**A.**4**B.**10**C.**14**D.**30

## Answers and explanations

**B.**The best way to solve this problem is to draw a graph. To get it right, you have to remember the meaning of slope:A slope of

for example, tells you to move 2 spaces up (the rise) and 5 spaces to the right (the run). You don’t have to be a great artist, just count the spaces. The function in this problem has a slope of 2, which is the same as

Starting at (–2, –3) and following these directions yields this graph:

**A.**When you see a quadratic expression in a problem, see whether it can be factored.*a*^{2}–*b*^{2}should look familiar to you: it factors out to (*a*–*b*) (*a*+*b*). Because*a*^{2}–*b*^{2 }= 40 and*a*–*b*= 10, (10) (*a*+*b*) = 40 so*a*+*b*= 4. Notice that you didn’t even have to figure out what*a*and*b*are to solve the problem, which happens a lot on the SAT.