Assignment page 535 - 537

(1 - 18, 36, 41 - 43) What is a zero of a function? Lesson 8-2 Characteristics of Quadratic Functions A zero of a function is an x-value that makes the function equal to 0. A zero of a function is the same as an x-intercept of a function.

A quadratic function may have one, two, or no zeros. What is the axis of symmetry? A vertical line that divides a parabola into two symmetrical halves is the axis of symmetry. The axis of symmetry always passes through the vertex of the parabola.

You can use the zeros to find the axis of symmetry.

If a function has one zero, use the x-coordinate to find the axis of symmetry.

If a function has two zeros, use the average of the two zeros to find the axis of symmetry. How can we find the vertex of a parabola? How do you find the axis of symmetry? Example 5: Application a) The graph of f(x) = –0.06x^2 + 0.6x + 10.26 can be used to model the height in meters of an arch support for a bridge, where the y-axis represents the water level and x represents the horizontal distance in meters from where the arch support enters the water. Can a sailboat that is 14 meters tall pass under the bridge? Explain.

b) The height of a small rise in a roller coaster track is modeled by

f(x) = –0.07x^2 + 0.42x + 6.37, where x is the distance in feet from a supported pole at ground level. Find the greatest height of the rise. Example 1A Finding Zeros of Quadratic Functions From Graphs y = x^2 + 8x + 16 y = –2x^2 – 2 y = –4x^2 – 2 y = x^2 – 6x + 9 Find the zeros of the quadratic function from its graph. Check your answer. y = x^2 – 2x – 3 B. Find the average of the zeros. Identify the x-coordinate of the vertex. A. Find the axis of symmetry of each parabola. Example 2: Finding the Axis of Symmetry by Using Zeros Find the average of the zeros. b. a. Identify the x-coordinate of the vertex. If a function has no zeros or they are difficult to identify from a graph, you can use a formula to find the axis of symmetry. The formula works for all quadratic functions.

For a quadratic function y = ax^2 + bx + c, the axis of symmetry is the vertical line x = -b/2a. Find the axis of symmetry of each parabola. Check It Out! Example 2 Step 2. Use the formula. y = –3x^2 + 10x + 9 Step 1. Find the values of a and b. Find the axis of symmetry of the graph of

y = –3x^2 + 10x + 9. Example 3: Finding the Axis of Symmetry by Using the Formula Step 2. Use the formula. y = 2x^2 + 1x + 3 Step 1. Find the values of a and b. Find the axis of symmetry of the graph of

y = 2x^2 + x + 3. Check It Out! Example 3 Step 3 Write the ordered pair. Step 2 Find the corresponding y-coordinate. Step 1 Find the x-coordinate of the vertex. The zeros are –6 and –2. y = 0.25x^2 + 2x + 3 Find the vertex. Example 4A: Finding the Vertex of a Parabola Step 1 Find the x-coordinate of the vertex. y = –3x^2 + 6x – 7 Find the vertex. Example 4B: Finding the Vertex of a Parabola Step 3 Write the ordered pair. Step 2 Find the corresponding y-coordinate. Check It Out! Example 4 Step 1 Find the x-coordinate of the vertex. y = x^2 – 4x – 10 Find the vertex. Step 3 Write the ordered pair. Step 2 Find the corresponding y-coordinate.

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# Lesson 8-2 Characteristics of Quadratic Functions

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