# Solving Quadratic Equations 9 5 by Graphing Objective

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Solving Quadratic Equations 9 -5 by Graphing Objective Solve quadratic equations by graphing. Holt Algebra 1

Solving Quadratic Equations 9 -5 by Graphing Lesson Quiz: Part I 1. Order the function f(x) = 4 x 2, g(x) = – 5 x 2, and h(x) = 0. 8 x 2 from narrowest graph to widest. g(x) = – 5 x 2, f(x) = 4 x 2, h(x) = 0. 8 x 2 2. Graph of f(x) = x 2 and g(x) =0. 5 x 2 – 2 on the same graph. How are they different/the same? • The graph of g(x) is wider. • Both graphs open upward. • Both have the axis of symmetry x = 0. • The vertex of g(x) is (0, – 2); the vertex of f(x) is (0, 0). Holt Algebra 1

Solving Quadratic Equations 9 -5 by Graphing Example 1 A: Solving Quadratic Equations by Graphing Solve the equation by graphing the related function. 2 x 2 – 18 = 0 Step 1 Write the related function. 2 x 2 – 18 = y, or y = 2 x 2 + 0 x – 18 Step 2 Graph the function. The axis of symmetry is x = 0. • The vertex is (0, – 18). • Two other points (2, – 10) and (3, 0) • Graph the points and reflect them across the axis of symmetry. • Holt Algebra 1 x=0 ● ● (3, 0) ● ● (2, – 10) ● (0, – 18)

Solving Quadratic Equations 9 -5 by Graphing Example 1 A Continued Solve the equation by graphing the related function. 2 x 2 – 18 = 0 Step 3 Find the zeros. The zeros appear to be 3 and – 3. Check 2 x 2 – 18 = 0 2(3)2 – 18 2(9) – 18 18 – 18 0 Holt Algebra 1 2 x 2 – 18 = 0 0 2(– 3)2 – 18 0 0 Substitute 3 and – 3 2(9) – 18 0 0 for x in the quadratic 18 – 18 0 0 equation.

Solving Quadratic Equations 9 -5 by Graphing Example 1 B: Solving Quadratic Equations by Graphing Solve the equation by graphing the related function. – 12 x + 18 = – 2 x 2 Step 1 Write the related function. y = – 2 x 2 + 12 x – 18 x=3 Step 2 Graph the function. The axis of symmetry is x = 3. • The vertex is (3, 0). • Two other points (5, – 8) and (4, – 2). • Graph the points and reflect them across the axis of symmetry. ● • Holt Algebra 1 ● ● ● (3, 0) ● (4, – 2) ● (5, – 8)

Solving Quadratic Equations 9 -5 by Graphing Example 1 B Continued Solve the equation by graphing the related function. – 12 x + 18 = – 2 x 2 Step 3 Find the zeros. The only zero appears to be 3. Check y = – 2 x 2 + 12 x – 18 0 – 2(3)2 + 12(3) – 18 0 – 18 + 36 – 18 0 0 You can also confirm the solution by using the Table function. Enter the function and press When y = 0, x = 3. The x-intercept is 3. Holt Algebra 1