Exercises for Question Type 1: Constructing simple graphs to solve equations

Question 1

Skill question

By sketching the graphs of $y = x^{2}$ and $y = 5 x - 4$ , find the solutions to $x^{2} = 5 x - 4$ .

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Question 2

Skill question

Sketch the graphs of $y = x^{2}$ and $y = x + 2$ , then solve $x^{2} = x + 2$ .

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Question 3

Skill question

Solve graphically the equation $x^{2} = 4 - x$ by sketching the graphs of $y = x^{2}$ and $y = 4 - x$ , and estimate the solutions. Verify your results algebraically.

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Question 4

Skill question

By plotting $y = x^{2}$ and $y = 3 x + 2$ , find graphically the solutions of $x^{2} = 3 x + 2$ .

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Question 5

Skill question

Sketch the graphs of $y = x^{2}$ and $y = - x + 4$ , then solve $x^{2} = - x + 4$ .

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Question 6

Skill question

Sketch the graphs of $y = x^{2}$ and $y = 2 x + 3$ , and hence find the exact solutions to the equation $x^{2} = 2 x + 3$ .

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Question 7

Skill question

By plotting $y = x^{2}$ and $y = 2 - 0.5 x$ , find the approximate solutions to $x^{2} = 2 - 0.5 x$ .

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Question 8

Skill question

Solve graphically the equation $x^{2} = - 3 x + 5$ by plotting $y = x^{2}$ and $y = - 3 x + 5$ , and give approximate solutions.

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Question 9

Skill question

Sketch $y = x^{2}$ and $y = 3$ , then determine graphically the solutions to $x^{2} = 3$ .

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Question 10

Skill question

Sketch the graphs of $y = x^{2}$ and $y = 2 x + 1$ , and hence solve $x^{2} = 2 x + 1$ .

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Question 11

Skill question

Solve graphically the equation $x^{2} = 6 - x$ by sketching the graphs of $y = x^{2}$ and $y = 6 - x$ , and state the values of $x$ .

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Question 12

Skill question

Solve graphically $x^{2} = - x + 2$ by drawing $y = x^{2}$ and $y = - x + 2$ , and state the solutions.

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IB Mathematics Analysis and Approaches Question Type 1: Constructing Simple Graphs to Solve Equations Exercises