Beginning Algebra, 11th Edition

SECTION 9.5 More on Graphing Quadratic Equations; Quadratic Functions 585

Complete solution available
on the Video Resources on DVD

9.5 EXERCISES

Give the coordinates of the vertex and sketch the graph of each equation. See Examples 1 and 2.

Decide from each graph how many real solutions has. Then give the solution set (of

real solutions). See Example 3.

19.Concept Check Based on your work in Exercises 1 – 12,what seems to be the direction

in which the parabola opens if? If?

20.Concept Check How many real solutions does a quadratic equation have if its

corresponding graph has (a)no x-intercepts, (b)one x-intercept, (c)two x-intercepts?

(See Examples 1 – 3.)

y=ax^2 +bx+c a 70 a 60

ƒ 1 x 2 = 0

y=-x^2 - 4 x- 3 y=x^2 + 4 x y=x^2 - 2 x

y=x^2 - 8 x+ 16 y=x^2 + 6 x+ 9 y=-x^2 + 6 x- 5

y= 1 x- 422 y=x^2 + 2 x+ 3 y=x^2 - 4 x+ 3

y=x^2 - 6 y=-x^2 + 2 y= 1 x+ 322

x

y

2 y = f(x)

(^02)
x
y
y = f(x)
0
–3
x
y
y = f(x)
–2^02
4
x
y
y = f(x)
–3^01
5
x
y
y = f(x)
2
(^02)
x
y
y = f(x)
0
–3
2
EXERCISES 21 – 22
The connection between the solutions of an equation and the x-intercepts of its graph
enables us to solve quadratic equations with a graphing calculator. With the equation in
the form , enter as , and then direct the calculator
to find the x-intercepts of the graph. (These are also referred to as zerosof the function.)
For example, to solve graphically, refer to the three screens
shown here. The displays at the bottoms of the lower two screens show the two
solutions:- 1 and 6.
x^2 - 5 x- 6 = 0
ax^2 +bx+c= 0 ax^2 +bx+c Y 1

TECHNOLOGY INSIGHTS

5

–15

–10 10

5

–15

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