Solving Quadratic Equations with the Quadratic Formula

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$   

• a = 2 , b = 3, c = -5

• a = 2, b = -3, c = 5

• a = 2, b = -3, c = -5

• a = -2, b = 3, c = 5

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Solutions of a quadratic equation are also called

• roots

• x-intercepts

• zeros

• All of the above

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The first step in solving quadratic equations is to . . .

• factor

• write the equation in standard form

• use quadratic formula

• complete the square

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Why are quadratic equations set equal to zero?

• Because zero is an easy number to work with.

• Because we are trying to find the x-intercepts and that happens when y=0.

• Because setting it equal to zero helps us find the y-intercepts.

• None of the above

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CCSS.HSA-REI.B.4B

Solve using the Quadratic Formula:
 $5x^2+3x-1=0$ 

•  $x=\frac{3\pm\sqrt{29}}{5}$  

•  $x=\frac{8}{5}\ or\ x=-\frac{2}{5}$  

•  $x=\frac{-3\pm\sqrt{29}}{10}$  

• No real solutions

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When does a quadratic equation have no real solutions?

• When you cannot factor it

• When it begins with a negative leading coefficient

• When there is a square root of a negative number

• When it only has two terms

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Check all of the following situations where you could use the Quadratic Formula to solve an equation.

• When its highest exponent (degree) is 1

• When its highest exponent (degree) is 2

• When its highest exponent (degree) is 3

• When you cannot factor the quadratic

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CCSS.HSA-REI.B.4B

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

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What should you do first in solving this equation?
x² + 6x - 13 = 3

• Get factored form
• Write down: a=1, b=6, c=-13
• Make it equal 0 by subtracting 3 on each side
• Type it all in a calculator.

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CCSS.HSA-REI.B.4B

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

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