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Find the zeros of a quadratic function from its graph. Find the axis of symmetry and the vertex of a parabola. Objectives

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Recall that an x-intercept of a function is a value of x when y = 0. A zero of a function is an x- value that makes the function equal to 0. So a zero of a function is the same as an x-intercept of a function. Since a graph intersects the x-axis at the point or points containing an x-intercept, these intersections are also at the zeros of the function. A quadratic function may have one, two, or no zeros.

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Example 1A: Finding Zeros of Quadratic Functions From Graphs Find the zeros of the quadratic function from its graph. Check your answer. y = x 2 – 2x – 3 The zeros appear to be –1 and 3. y = (–1) 2 – 2(–1) – 3 = – 3 = 0 y = 3 2 –2(3) – 3 = 9 – 6 – 3 = 0 y = x 2 – 2x – 3 Check

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Example 1B: Finding Zeros of Quadratic Functions From Graphs Find the zeros of the quadratic function from its graph. Check your answer. y = x 2 + 8x + 16 y = (–4) 2 + 8(–4) + 16 = 16 – = 0 y = x 2 + 8x + 16 Check The zero appears to be –4.

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Example 1C: Finding Zeros of Quadratic Functions From Graphs Find the zeros of the quadratic function from its graph. Check your answer. y = –2x 2 – 2 The graph does not cross the x-axis, so there are no zeros of this function.

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Find the axis of symmetry of each parabola. A. (–1, 0) Identify the x-coordinate of the vertex. The axis of symmetry is x = –1. Find the average of the zeros. The axis of symmetry is x = 2.5. B.

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Y= x 2 + 4x - 21 Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. The graph of y = x 2 + 4x – 21 shows that two zeros appear to be –7 and 3, the same as the solutions from factoring. ●●

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Y= x 2 – 12x + 36 Check Graph the related quadratic function. The graph of y = x 2 – 12x + 36 shows that one zero appears to be 6, the same as the solution from factoring. ●

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Y=x 2 + 4x - 5 Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. The graph of y = x 2 + 4x – 5 shows that the two zeros appear to be 1 and –5, the same as the solutions from factoring. ● ●

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