1
Proceed as in Exercise 21 with the quadratic function x^2 + 3x + 1: where does its graph cross the x-axis, and where the function axis?
Chapter 22 · Graphical Solution of Equations in One Unknown
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
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From Graph of a Quadratic Function, exercise 22
Exercises 19 and 20 cannot be solved by the factoring previously explained. They have irrational roots, but the approximate values of the roots can be obtained graphically. Solve them graphically.
From Graph of a Quadratic Function, exercise 20
Exercises 19 and 20 cannot be solved by the factoring previously explained. They have irrational roots, but the approximate values of the roots can be obtained graphically. Solve them graphically.
2
x^2 + 2x = 5
From Imaginary Roots and the Graph, exercise 4
If possible, solve graphically (type none if the equation has no real root):
3
2x^2 + x - 1 = 0
From Graph of a Quadratic Function, exercise 17
Solve Exercises 16 and 17 graphically and check each by substituting in the original equation; or solve by factoring and compare.
4
x^2 - 4x + 4 = 0
From Imaginary Roots and the Graph, exercise 2
If possible, solve graphically (type none if the equation has no real root):
5
x^2 - 6x + 11 = 0
From Graph of a Quadratic Function, exercise 1
Exercises 1, 4, 7, and 9 refer to the graph of f(x) = 4x^2 - 4x - 15 in the lesson.
6
Read from the graph the values of x for which 4x^2 - 4x - 15 equals zero.
From Functions and the Graph of a Linear Function, exercise 1
Exercises 1–8 refer to the graph of f(x) = 2x + 3 in the lesson.
7
Read from the graph the value of x when f(x) is zero.
From Graph of a Quadratic Function, exercise 3
Exercises 1, 4, 7, and 9 refer to the graph of f(x) = 4x^2 - 4x - 15 in the lesson.
8
Compare the answers to Exercises 1 and 2. Are they the same?
From Functions and the Graph of a Linear Function, exercise 11
Exercises 1–8 refer to the graph of f(x) = 2x + 3 in the lesson.
9
From the graph of Exercise 9 read the roots of: (a) 5 - 2x = 9; (b) 5 - 2x = 5; (c) 5 - 2x = -3; (d) 5 - 2x = -7.
From Graph of a Quadratic Function, exercise 19
Exercises 19 and 20 cannot be solved by the factoring previously explained. They have irrational roots, but the approximate values of the roots can be obtained graphically. Solve them graphically.
10
x^2 - 2x = 2