# SAT Math: A Challenging Quadratic Function Problem

As you prepare for the SAT, you’ll definitely want to review quadratic functions. You’ll need to know how to solve quadratic equations, as well as understand the properties of the graphs of these functions.

Here’s a challenging problem involving a quadratic function. Give it a try and then scroll down for the solution.

f(x) = a(x + b)(x – 8)

The equation above represents a quadratic function where a and b are constants. If the function is graphed in the xy-plane, its vertex is at the point (2, -54). What is the value of a + b?

(A)  4
(B)  5.5
(C)  6
(D)  7.5

# SAT Math: Focus on Quadratics & Parabolas

This book will be the first in a series that addresses the topics that appear most frequently in the Math section of the New SAT. You’ll get a chance to review the most important concepts of quadratic equations and the graphs of parabolas. Then you’ll apply what you know to 25 problems — some done without your calculator and some with, just as it is on test day. Each problem comes with a full explanation of how to arrive at the correct answer.

We’d like to help as many students as possible achieve success on the SAT, so we’ve made the price of this volume just \$0.99.

The book can be purchased on Amazon by clicking on the image to the left or going here.

# SAT Math: Quadratics & Parabolas

The focus of the new SAT Math test is on concepts of algebra more than it has been in the past. One of the things you’ll want to know well is how to work with quadratic equations and their graphs, which are parabolas. You’ll need to be able to solve quadratic equations by factoring and by using the Quadratic Formula. You’ll also need to know about the different forms of the equation for a parabola and about the properties of parabolas.

At the bottom of this post you’ll find a link to ten SAT practice problems involving quadratics and parabolas. There’s a second link down there to the solutions as well.

But first, let’s review some of the important characteristics of quadratic functions and their graphs.

# SAT Math: A Challenging Functions Problem

As my students and I have prepared for the new SAT, one of the things we’ve noticed is that the more challenging Math problems aren’t just computational or problems where you can throw something into your calculator to get the answer. They are more theoretical — you have to really know the math in order to come up with the correct answer.

Let’s consider a challenging problem involving functions.

A function is defined by the equation below.

f(x) = a(x – 2)(x – 10)

If the minimum value of the function is -8, what is the value of a?

A)  -2
B)  1/4
C)  1/2
D)  2