Over Lesson 4–1

A. maximum

B. minimum

Does the function f(x) = 3x2 + 6x have a maximum or a minimum value?

Over Lesson 4–1

A. –1

B. 0

C. 1

D. 2

Find the y-intercept of f(x) = 3x2 + 6x.

Over Lesson 4–1

A. x = y + 1

B. x = 2

C. x = 0

D. x = –1

Find the equation of the axis of symmetry for f(x) = 3x2 + 6x.

Over Lesson 4–1

A. 1

B. 0

C. –1

D. –2

Find the x-coordinate of the vertex of the graph of the function f(x) = 3x2 + 6x.

Over Lesson 4–1

Graph f(x) = 3x2 + 6x.

A. ans B.

C. ans D. ans

Over Lesson 4–1

Which parabola has its vertex at (1, 0)?

A. y = 2x2 – 4x + 3

B. y = –x2 + 2x – 1

C. y = x2 + x + 1

D. y = 3x2 – 6x

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Two Real Solutions

Solve x2 + 6x + 8 = 0 by graphing.

Graph the related quadratic function f(x) = x2 + 6x + 8.

The equation of the axis of symmetry is x = –3.

Make a table using x-values around –3.

Then graph each point.

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.

Check Check the solutions by substituting each solution into the original equation to see if it is satisfied.

x

2 + 6x + 8 = 0 x

2 + 6x + 8 = 0

0 = 0 0 = 0

(–4)2 + 6(–4) + 8 = 0 (–2)2 + 6(–2) + 8 = 0? ?

Solve x2 + 2x – 3 = 0 by graphing.

A. B.

C. D.

–3, 1 –1, 3

–3, 1 –1, 3

One Real Solution

Solve x2 – 4x = –4 by graphing.

Write the equation in ax2 + bx + c = 0 form.

x2 – 4x = –4 x2 – 4x + 4 = 0 Add 4 to each side.Graph the related quadratic function f(x) = x2 – 4x + 4.

One Real Solution

Notice that the graph has only one x-intercept, 2.

Answer: The only solution is 2.

Solve x2 – 6x = –9 by graphing.

A.B.

C.D.

–3

3 3

–3

Estimate Roots

Solve –x2 + 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.

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.

A. 0 and 1, 3 and 4

B. 0 and 1

C. 3 and 4

D. –1 and 0, 2 and 3

Solve x2 – 4x + 2 = 0 by graphing. What are the consecutive integers between which the roots are located?