Objective Solve quadratic equations by graphing.

Lesson Quiz: Part I 1. Order the function f(x) = 4x2, g(x) = –5x2, and h(x) = 0.8x2 from narrowest graph to widest. 2. Graph of f(x) = x2 and g(x) =0.5x2 –2 on the same graph. How are they different/the same? g(x) = –5x2, f(x) = 4x2, h(x) = 0.8x2 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).

Example 1A: Solving Quadratic Equations by Graphing Solve the equation by graphing the related function. 2x2 – 18 = 0 Step 1 Write the related function. 2x2 – 18 = y, or y = 2x2 + 0x – 18 Step 2 Graph the function. x = 0 ● ● 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. (3, 0) ● ● (2, –10) ● (0, –18)

Example 1A Continued Solve the equation by graphing the related function. 2x2 – 18 = 0 Step 3 Find the zeros. The zeros appear to be 3 and –3. 0 0 Check 2x2 – 18 = 0 2(3)2 – 18 0 2(9) – 18 0 18 – 18 0  2x2 – 18 = 0 2(–3)2 – 18 0 2(9) – 18 0 18 – 18 0  Substitute 3 and –3 for x in the quadratic equation.

Example 1B: Solving Quadratic Equations by Graphing Solve the equation by graphing the related function. –12x + 18 = –2x2 Step 1 Write the related function. y = –2x2 + 12x – 18 x = 3 Step 2 Graph the function. (3, 0) ● ● ● 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. (4, –2) ● (5, –8) ●

Example 1B Continued Solve the equation by graphing the related function. –12x + 18 = –2x2 Step 3 Find the zeros. The only zero appears to be 3. Check y = –2x2 + 12x – 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.