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Course: Praxis Core Math > Unit 1

Lesson 4: Algebra
Test prep
Praxis Core Math
Lessons
Algebra
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Quadratic equations | Lesson

Google Classroom

What are quadratic equations?

A quadratic equation is an equation with at least one
as its highest power term and one or more constants. For example, in the quadratic equation 3x2=48:
  • x is the variable, which represents a number whose value we don't know yet.
  • The 2 is the power or exponent. An exponent of 2 means the variable is
    .
  • 3 is the coefficient, or the constant multiple of x2. Together, 3x2 is a single
    .
  • 48 is a constant. It is a term as well.
Although quadratic equations often contain both terms to the second power and
, the test only covers quadratic equations with terms to the second power and constants.
Solving a quadratic equation means finding the value(s) for the variable(s) that make the equation true. To do that, we need to first understand how to work with squares and square roots.

What skills are tested?

  • Calculating the squares and square roots of numbers
  • Solving quadratic equations with one variable

What are squares and square roots?

The square of a number is equal to the number multiplied by itself. For example:
32=3×3
The square root of a positive number x, written as x, is the answer to the question "what positive number squared equals x ?" For example, since 32=9, the square root of 9, or 9, is 3.
For numbers greater than or equal to 0, squaring and taking the square root are
. This means if we perform both operations on a number in succession, the result would be the original number. For example:
32=(3)2=3

How do we solve quadratic equations?

For quadratic equations in the form x2=c, we can solve for x by taking the square root of both sides of the equation:
x=±c
For quadratic equations with coefficients and constants, we need to rearrange the equation until it's the form x2=c, then take the square root of both sides of the equation.
For example, to solve 3x2=300, we must first divide both sides of the equation by 3 before taking the square root.

Your turn!

TRY: PERFECT SQUARE
If x2=9, which of the following could be the value of x ?
Choose 1 answer:

TRY: PERFECT SQUARE
For x>0, if x2=169, what is the value of x ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

TRY: SOLVING QUADRATIC EQUATION
If 2x2=50, which of the following could be the value of x ?
Choose all answers that apply:

TRY: TRANSLATING AND SOLVING QUADRATIC EQUATION
If 5 times the square of a certain number is 80, which of the following could be that number?
Choose 1 answer:

Things to remember

Note: All of the following assume x≥0.
x2=x×x
x is the answer to the question "what number squared equals x ?"
x2=(x)2=x
To solve a quadratic equation by taking the square root, we:
  1. Rearrange the equation to isolate x2.
  2. Take the square root of both sides of the equation to find x.
The solution to x2=c is x=±c.

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