SECTION 6.5 Solving Equations by Factoring 353
EXERCISES 75 – 76
The solutions of the quadratic equation are represented on
the graph of the quadratic function by the x-intercepts.
Use the zero-factor property to solve each equation, and confirm that your
solutions correspond to the x-intercepts (zeros) shown on the accompanying graphing
calculator screens. See the Connections box.
75.
76.-x^2 + 3 x=- 10
2 x^2 - 7 x- 4 = 0
ƒ 1 x 2 =ax^2 +bx+c
ax^2 +bx+c= 0 1 aZ 02
TECHNOLOGY INSIGHTS
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EXERCISES 77– 82
If air resistance is neglected, the height (in feet) of an object projected directly
upward from an initial height feet with initial velocity (speed) feet per second is
where x is the number of seconds after the object is projected.
Suppose that a ball is projected directly upward from an initial height of 100 ft
with an initial velocity of 80 ft per sec. Use this information and a graphing calculator
to answer the following. Work Exercises 77 – 82 in order.
77.Define a function that describes the height of the ball in terms of time x.
78.Use a graphing calculator to graph the function from Exercise 77.Use domain
and range
79.Use the graph from Exercise 78and the tracing capability of the calculator to
estimate the maximum height of the ball. When does it reach that height?
80.After how many seconds will the ball reach the ground (that is, have height 0 ft)?
Estimate the answer from the graph and check it in the equation.
81.Use the graph to estimate the time interval during which the height of the ball is
greater than 150 ft. (Hint:Also graph .) Check your estimate by
substituting it into the function from Exercise 77.
82.Define a function that describes the height of an object if the initial velocity is
100 ft per sec and the object is projected from ground level.
g 1 x 2 = 150
3 0, 10 4 3 - 100, 300 4.
ƒ 1 x 2 =- 16 x^2 +v 0 x+s 0 ,
s 0 v 0
ƒ 1 x 2
RELATING CONCEPTS
