# 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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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

FF(x)=ax 2 +bx+c FFrom 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)

 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

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

Line of Symmetry Distance of roots from the Line of Symmetry

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

a = 5b = -1c = -4

Enter this Part Into Your Calculator

Simplify

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

 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

 Fill in the quadratic formula:

You should have gotten:

These are The Roots/Zeros

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

 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***

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

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

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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