Quadratic Equation Review

Solving Quadratic Equations Review

By Graphing

• Look for the x-intercepts

• Zeros, Roots, Solutions are all x-intercepts.

Multiple Choice

How many solutions does this function have?

• two

• one

• all real numbers

• no real solutions

Multiple Choice

What are the solutions of this graph?

• -2 and 3

• -1/2 and -6

• -2 and -6

• 3 and -6

Multiple Choice

Name the x-intercept(s)?

• 0

• 4

• 2

• 0 and 4

Multiple Choice

Which is a zero of the graph?

• 0

• -1

• 1.5

• -3

Solve by Factoring

• Try to factor

• Graph and look for solutions

• 
  

Multiple Choice

Solve by factoring: x² = 7x + 18

• -7 and -18

• 9 and 2

• 9 and -2

• 2 and 7

Multiple Choice

What are the factors AND solutions of x² + 2x – 3 = 0

• (x - 2)(x + 1); x=2, x=-1
• (x + 1)(x - 3); x=-1, x=3
• (x + 2)(x - 1); x=-2, x=1
• (x - 1)(x + 3); x=1, x=-3

Multiple Choice

Factor x²-6x-40

• (x-10)(x+4)
• (x+10)(x-4)
• (x-8)(x+5)
• (x+8)(x-5)

Solving by Square Root Method

• Isolate the square on one side.

• Take the square root to solve.

• Remember the square root has a negative/positive solution

Multiple Choice

Solve the equation using square roots.

x² = 121

• 60.5

• ± 11

• ± 12

• 11

Multiple Choice

Find the x-intercept(s) by taking square roots.
$$\left(x-1\right)^2=6$$  

• $$\left\{\pm\sqrt{6}-1\right\}$$  

• $$\left\{1\pm\sqrt{6}\right\}$$  

• $$\left\{37\right\}$$  

• $$\left\{1\pm\sqrt{3}\right\}$$   

Multiple Choice

$$3\left(x-4\right)^2=48$$  

• $$x=\pm8$$  

• $$x=4\pm3\sqrt{5}$$  

• $$x=-8$$  

• $$x=8,\ 0$$  

Quadratic Formula

• Put the equation in standard form

• Identify the values of a, b, and c

• Plug in the formula

Multiple Choice

Identify the a,b, and c-values of the following quadratic equation: $$3x^2=-2x+1$$

• $$a=3,\ b=-2,\ c=1$$  

• $$a=3,\ b=2,\ c=-1$$  

• $$a=3x^2,\ b=-2x,\ c=1$$  

• $$a=3x^2,\ b=2x,\ c=1$$  

Multiple Choice

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

Solve using the Quadratic Formula:

$$2x^2+7x-15=0$$  

• $$x=-1.5,\ 5$$  

• No Solution

• $$x=-5,\ 1.5$$  

• $$x=0.7,\ 5$$  

Multiple Choice

Use the quadratic formula to find the roots of this equation:  $$x^2+3x=5$$  

• $$\frac{-3\pm\sqrt{29}}{2}$$  

• $$\frac{3\pm\sqrt{29}}{2}$$  

• $$\frac{-3\pm\sqrt{-11}}{2}$$  

• $$\frac{3\pm\sqrt{-11}}{2}$$  

Multiple Choice

Solve by the Quadratic Formula:

$$9u^2-11u+7=0$$  

• $$\frac{-11\pm\sqrt{441}}{18}$$  

• $$\frac{11\pm\sqrt{441}}{18}$$  

• $$\frac{11\pm\sqrt{131}}{-18}$$  

• $$\frac{11\pm i\sqrt{373}}{18}$$