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What are you finding when you solve the quadratic formula? Where the graph crosses the x-axis Also known as: Zeros, Roots and X-intercepts

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FF(x)=ax 2 +bx+c FFrom previous courses you learned that if: a is positive (a>0) then C is the y-intercept: The parabola opens up a is negative (a<0) thenThe parabola opens down (0, c)

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What shape is the graph? How do you know? Which way does the graph the graph open? Why? What is the y-intercept? Why? Parabola because of the x 2 Open up because of the 5 in front of x 2 (0, -4) because c = -4

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You need to make sure that your equation is in standard form and equal to 0 in order to use Quadratic Formula. QUADRATIC FORMULA Always opposite of b Always a 2 Always a 4 Always a 2

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Line of Symmetry Distance of roots from the Line of Symmetry

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In order to use the Quadratic Formula you need to determine the values of a, b, and c. What is a equal to? What is b equal to? What is c equal to? A=5 B= -1 C=-4

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a = 5b = -1c = -4

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Enter this Part Into Your Calculator

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Simplify

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Zeros, Roots and X-Intercepts You have to do + and then -

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Which way does your parabola open? Why? What is the y-intercept? Why? What are the values of a, b and c? Opens up because 2 is positive (0, -32) because c= -32 a = 2 b = 12 c = -32

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Fill in the quadratic formula:

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You should have gotten:

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These are The Roots/Zeros

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Answer: 0 times1 timeor2 times Using the Quadratic Formula how can we tell? The value under the square root (b 2 - 4ac) tells us: If it is positive: If it is 0: If it is negative: There are 2 roots There is 1 roots There are 0 roots

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1x 2 + 8x + 12 = 0 b 2 - 4ac 8 2 – 4*1*12 = 162 roots 1x 2 + 8x + 16 = 0 b 2 - 4ac 8 2 – 4*1*16 = 01 root 1x 2 + 8x + 20 = 0 b 2 - 4ac 8 2 – 4*1*20 = -160 roots ***Graph each equation and check the number of roots***

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Answer: On the line of symmetry The line of symmetry can be substituted in for x or y to find the vertex? For X!!!

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What is the line of symmetry? Where do you put 1/10 into the equation? For X!!! Put your answer in an ordered pair:

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What is the line of symmetry? Where do you put -3 into the equation? For X!!! Put your answer in an ordered pair:

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Factor and Solve: 1.x² - 6x – 27 = 0 2.4x² - 1 = 0 Convert to Vertex Format by Completing the Square (hint: kids at the store) 3. Y = 3x² - 12x + 20.

Factor and Solve: 1.x² - 6x – 27 = 0 2.4x² - 1 = 0 Convert to Vertex Format by Completing the Square (hint: kids at the store) 3. Y = 3x² - 12x + 20.

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