Warm-up
Evaluate each ex pression if a = 6, b = -2, and c = 12.

Today we will:
1. Solve problems about situations modeled by parabolas . Last section in the
book!

Following class period we will:
1. Review key concepts

o Quadratic equation – an equation that can written in the form an equation
0 = ax2 + bx + c, where a, b, and c are numbers and a ≠ 0.

o Quadratic formula – the formula is used to find the solutions of a
equation.

Today we will solve the quadratic equations by…
• Graphing (the x- intercepts are the solutions )

Solving 0 = ax2 + bx + c by graphing
The solutions to 0 = ax2 + bx + c are the x-intercepts of the graph of the
equation
y = ax2+ bx + c.

One way to solve is by drawing an accurate graph. If the graph doesn’t cross
the x-axis at points that correspond to integral units on the grid, the solutions
will be approximations.

Example 1:
Solve 10x2 - 5x –50 = 0 by graphing

Solution - Graph the quadratic function 10x2 - 5x –50 = y
Step 1 – Make a table of values.

Step 2 – Use the table to draw a graph

Step 3 – Read the x-intercepts from the graph.
The x-intercepts are at –2 and 2.5,
so the solutions of 10x2 - 5x –50 = 0 are x = -2 and x = 2.5.

Check your solution. Substitute –2 and 2.5 into the original equation.

Using the quadratic formula to solve ax2+ bx + c = 0

Unlike graphing where approximate solutions may be necessary, the quadratic
formula gives exact solutions to any equation ax2+ bx + c = 0.

Often the solutions involve square roots of numbers that are not perfect
squares. In such cases, you can approximate the solutions or give the exact
solutions in square root form.

Example 2:
Use the quadratic formula to solve 2x2+ 5x = 25

Solution
Step 1 - Write the equation in the form ax2+ bx + c = 0 and de termine the
values of a , b, and c.

Step 2 – Use the quadratic formula.

Check your solutions – substitute 2.5 and –5 in the original equation.

Example 3:
Use the quadratic formula to solve 0 = x2 - 11x + 18

Solution
Step 1 - Determine the values of a, b, and c.

Step 2 – Use the quadratic formula.

Check your solutions – substitute 9 and 2 in the original equation.
Yep, both work!

In Summary…
To solve quadratic equations we can…
• Graph to find the x-intercepts
• Factor ( and use the Zero - Product Property )

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of June 20th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!