Over Lesson 4–1 5-Minute Check 1 A.maximum B.minimum Does the function f(x) = 3x 2 + 6x have a maximum or a minimum value?

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Over Lesson 4–1 5-Minute Check 1 A.maximum B.minimum Does the function f(x) = 3x 2 + 6x have a maximum or a minimum value?

Over Lesson 4–1 5-Minute Check 2 A.–1 B.0 C.1 D.2 Find the y-intercept of f(x) = 3x 2 + 6x.

Over Lesson 4–1 5-Minute Check 3 A.x = y + 1 B.x = 2 C.x = 0 D.x = –1 Find the equation of the axis of symmetry for f(x) = 3x 2 + 6x.

Over Lesson 4–1 5-Minute Check 4 A.1 B.0 C.–1 D.–2 Find the x-coordinate of the vertex of the graph of the function f(x) = 3x 2 + 6x.

Over Lesson 4–1 5-Minute Check 5 Graph f(x) = 3x 2 + 6x. A.ansB. C.ansD.ans

Over Lesson 4–1 5-Minute Check 6 Which parabola has its vertex at (1, 0)? A.y = 2x 2 – 4x + 3 B.y = –x 2 + 2x – 1 C.y = x 2 + x + 1 D.y = 3x 2 – 6x __ 1 2

Example 1 Two Real Solutions Solve x 2 + 6x + 8 = 0 by graphing. Graph the related quadratic function f(x) = x 2 + 6x + 8. The equation of the axis of symmetry is x = –3. Make a table using x-values around –3. Then graph each point.

Example 1 Two Real Solutions We can see that the zeros of the function are –4 and –2. Answer: The solutions of the equation are –4 and –2. CheckCheck the solutions by substituting each solution into the original equation to see if it is satisfied. x 2 + 6x + 8 = 0 0 = 0 (–4) 2 + 6(–4) + 8 = 0 (–2) 2 + 6(–2) + 8 = 0 ??

Example 1 Solve x 2 + 2x – 3 = 0 by graphing. A.B. C.D. –3, 1–1, 3 –3, 1–1, 3

Concept

Example 2 One Real Solution Solve x 2 – 4x = –4 by graphing. Write the equation in ax 2 + bx + c = 0 form. x 2 – 4x = –4x 2 – 4x + 4 = 0Add 4 to each side. Graph the related quadratic function f(x) = x 2 – 4x + 4.

Example 2 One Real Solution Notice that the graph has only one x-intercept, 2. Answer: The only solution is 2.

Example 2 Solve x 2 – 6x = –9 by graphing. A.B. C.D. –3 33

Example 4 Estimate Roots Solve –x 2 + 4x – 1 = 0 by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. Make a table of values and graph the related function.

Example 4 Estimate Roots The x-intercepts of the graph are between 0 and 1 and between 3 and 4. Answer: One solution is between 0 and 1 and the other is between 3 and 4.

Example 4 A.0 and 1, 3 and 4 B.0 and 1 C.3 and 4 D.–1 and 0, 2 and 3 Solve x 2 – 4x + 2 = 0 by graphing. What are the consecutive integers between which the roots are located?