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**Graphing Quadratic Functions**

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**2 Forms of Quadratic Equations**

y = ax2 + bx + c y = a(x – h)2 + k Standard Form Vertex Form

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**The axis of symmetry for the parabola is the vertical line through the vertex.**

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**Graphing Using Vertex Form**

y = a(x – h)2 + k Vertex: (h, k) Axis of symmetry: x = h VERTICAL LINE If a is positive, then it opens up. If a is negative, then it opens down.

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**Graphing Using Vertex Form**

Find and sketch the axis of symmetry (opposite of h). Find and plot your vertex (opposite of h, same as k). Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)

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**Graphing Using Vertex Form**

Use Symmetry to plot the points on the opposite side of your axis of symmetry. Connect them with a U-shaped curve

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**f(x)= -3(x – 2)2 + 5 a = -3 h = 2 k = 5 Opens DOWN**

Tell whether it opens up or down, axis of symmetry, and name the vertex. f(x)= -3(x – 2)2 + 5 y = a(x – h)2 + k. a = -3 h = 2 k = 5 Opens DOWN Axis of symmetry: x = 2 Vertex: (2, 5)

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**f(x) = (x + 4)2 – 6 k = -6 a = 1 h = -4 Opens UP**

You try… Tell whether it opens up or down, axis of symmetry, and name the vertex. f(x) = (x + 4)2 – 6 k = -6 a = 1 h = -4 Opens UP Axis of symmetry: x = -4 Vertex: (-4, -6)

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OPENS UP Graph h = -5 k = -4 x 2(x + 5)2 - 4 y (x, y)

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Graph h = 3 k= 1 OPENS DOWN x y (x, y)

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**Graphing Using Standard Form**

*Once it is in standard form: Find and sketch the axis of symmetry using Find your vertex by substituting your axis of symmetry back into the original equation and solve for y.

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**Graphing Using Standard Form**

4. Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value) 5. Use Symmetry to plot the points on the opposite side of your axis of symmetry. Connect them with a U-shaped curve *Remember: If a is positive, it opens up, if a is negative, it opens down.

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OPENS UP Graph a = 1 b = 8 c = 13 x (x)2 + 8x + 13 y (x, y)

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Graph a = -1 b = 2 c = 0 OPENS DOWN x -(x)2 + 2x y (x, y)

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**Converting From Vertex Form to Standard Form:**

y = (x – 3)2 + 5 Step 1: FOIL the binomial Step 2: Multiply the “a” term by what you just foiled Step 3: combine like terms!

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**Convert the following to standard form:**

y = 2(x – 4)2 + 6

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**Convert the following to standard form:**

y = (x + 3)² + 4

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**Converting From Standard Form to Vertex Form**

Step 1: Identify a, b, and c Step 2: find the vertex (h, k) x-coordinate (h) = y-coordinate (k) = substitute the value you found for the x coordinate. Step 3: Substitute a, h, and k into vertex form!

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**Convert the following to vertex form:**

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**What is the vertex form of a parabola whose standard form equation is:**

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**Convert the following to vertex form:**

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