# Solving Quadratic Equations and Graphing Squares

Section 8.2

#12 solve each equation by using the quadratic formula (what is this quadratic formula? Don't understand how this is done)

M^2 + 2m = 8

#20 Solve each equation by using the quadratic formula

4 + 20x = 25x^2

#28 solve each equation by using the quadratic formula

2y^2 + 1 = 2y

#42 Number solutions. Find b^2 - 4ac and the number of real solutions to each equation

9m^2 + 16 = 24m

#50 ½ x^2 + x = 1

#80 Find two real numbers that have a sum of 8 and a product of 2

Section 8.3

#6 Writing a quadratic equation with given solutions. For each given pair of numbers find a quadratic equation with integral coefficients that has the numbers as its solutions.

-8, 2

#24 Using the discriminant in factoring. Use the discriminant to determine whether each quadratic polynomial can be factored, then factor the ones that are not prime.

8x^2 + 6x - 27

#32 Equations Quadratic in form

(3a + 2)^2 - 3(3a + 2) = 10

#54 Find all real solutions to each equation

2x - 5√x + 2 = 0

Section 9.1

#10 Linear and constant functions. Graph each function and state its domain and range.

G(x) = x + 2

#20 Absolute value functions. Graph each absolute value function and state its domain and range.

F(x) = | x - 2|

#34 Quadratic functions. Graph each quadratic function and state its domain and range

Y = -2x^2 + 3

#38 square root functions. Graph each square root function and state its domain and range

F(x) = √x + 1

#56 Graphing relations. Graph each relation and state its domain and range

X = -3

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Section 8.2

#12 solve each equation by using the quadratic formula (what is this quadratic formula? Don't understand how this is done)

m^2 + 2m = 8

Solution. m^2 + 2m - 8 =0

By the formula, we get

So,

or

#20 Solve each equation by using the quadratic formula

4 + 20x = 25x^2

Solution: The equation can be rewritten as 25x^2-20x-4=0

So,

So, or

#28 solve each equation by using the quadratic formula

2y^2 + 1 = 2y

Solution. 2y^2 + 1 = 2y 2y^2 -2y + 1 = 0

Since , it has no real solutions.

#42 Number solutions. Find b^2 - 4ac and the number of real solutions to each equation

9m^2 + 16 = ...

#### Solution Summary

The expert solves the quadratic equations and graphic squares.