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**Do Now 4/13/10 Take out homework from yesterday.**

Text p. 632, #3-5, 12 – 32 multiples of 4, #40 Copy HW in your planner. Practice worksheet 10.2 evens

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**Homework Text p. 632, #3-5, 12 – 32 multiples of 4, #40**

3) C 4) A 5) B 12 – 32) graphs 40) a) domain: -32 ≤ x ≤ 32 b) range: 0 ≤ y ≤

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Objective SWBAT graph y = ax² + bx + c

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**Section 10.2 “Graph y = ax² + bx + c”**

Properties of the Graph of a Quadratic Function y = ax² + bx + c is a parabola that: -opens up if a > 0 -opens down if a < 0 -is narrower than y = x² if the |a| > 1 -is wider than y = x² if the |a| < 1 -has an axis of x = -(b/2a) -has a vertex with an x-coordinate of -(b/2a) -has a y-intercept of c. So the point (0,c) is on the parabola

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**Finding the Axis of Symmetry and the Vertex of a Parabola**

Consider the graph y = -2x² + 12x – 7 (a) Find the axis of symmetry of the graph (b) Find the vertex of the graph Axis of symmetry: Substitute a = -2 b = 12 Substitute the x-value into the original equation and solve for y. The vertex of the parabola is the point (3,11)

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**Graph y = 3x² - 6x + 2 Step 1: Determine if parabola opens up or down**

Step 2: Find and draw the axis of symmetry Step 3: Find and plot the vertex Step 4: Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values. x y 2 -1 11 Step 5: Reflect the points plotted over the axis of symmetry. Step 6: Draw a parabola through the plotted points. Minimum Value

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**Graph y = -1/4x² - x + 1 Step 1: Determine if parabola**

opens up or down DOWN Step 2: Find and draw the axis of symmetry Step 3: Find and plot the vertex Step 4: Plot two points. Choose two x-values more than the x-coordinate of the vertex. Then find the corresponding y-values. x y 1 2 -2 Step 5: Reflect the points plotted over the axis of symmetry. Maximum Value Step 6: Draw a parabola through the plotted points.

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**Minimum and Maximum Values**

For y = ax² + bx + c, the y-coordinate of the vertex is the MINIMUM VALUE of the function if a > 0 or the MAXIMUM VALUE of the function if a < 0. y = ax² + bx + c; a > 0 y = -ax² + bx + c; a < 0 maximum minimum

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Homework Practice worksheet 10.2 form B evens

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EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x 2 + 12x – 7. a. Find the axis of symmetry of the graph of the function.

EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x 2 + 12x – 7. a. Find the axis of symmetry of the graph of the function.

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