Graphing Quadratic Equations in Two Variables Quiz
The question sheet
Reveal any answer as you study-
How do quadratic equations differ from linear equations?
- They include a squared variable term
- They use only addition
- They have no constant
- They cannot be graphed
Reveal answer
Answer: They include a squared variable term
Source evidence
PDF page 1164: 2 Quadratic equations are equations of the form ax + bx + c = 0 , where a ≠ 0 . They differ from linear equations by including a term with the variable raised to the second power. We use different methods to solve quadratic equations than linear equations, because just adding, subtracting, multiplying, and dividing terms will not isolate the variable. We have seen that some quadratic equations can be solved by factoring. In this chapter, we will use three other methods to solve quadratic equations. 2
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According to the Square Root Property, if x² = k and k ≥ 0, then:
- x = k/2
- x = 2k
- x = √k or x = −√k
- x = k only
Reveal answer
Answer: x = √k or x = −√k
Source evidence
PDF page 1164: If x = k , and k ≥ 0 , then x = k or x = − k .
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The Square Root Property gives how many solutions for x² = k?
- Two
- One
- Three
- Zero
Reveal answer
Answer: Two
Source evidence
PDF page 1164: 2 Notice that the Square Root Property gives two solutions to an equation of the form x = k : the principal square root of
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What are the solutions to x² = 9?
- x = 3 only
- x = 81
- x = 3, x = −3
- x = 9, x = −9
Reveal answer
Answer: x = 3, x = −3
Source evidence
PDF page 1164: Rewrite to show the two solutions. x = 3, x = −3
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To use the Square Root Property, the coefficient of the variable term must equal:
- 0
- 1
- k
- 2
Reveal answer
Answer: 1
Source evidence
PDF page 1166: To use the Square Root Property, the coefficient of the variable term must equal 1. In the next example, we must divide both sides of the equation by 5 before using the Square Root Property.
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When solving (x − 3)² = 16, the binomial (x − 3) is treated as:
- The quadratic term
- A constant
- The radical
- A coefficient
Reveal answer
Answer: The quadratic term
Source evidence
PDF page 1168: 2 We can use the Square Root Property to solve an equation like (x − 3) = 16 , too. We will treat the whole binomial, (x − 3) , as the quadratic term.
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In Example 10.12, p² − 10p + 25 = 18, the left side is factored as:
- (p + 5)²
- (p − 5)²
- (p − 18)
- (p − 25)
Reveal answer
Answer: (p − 5)²
Source evidence
PDF page 1171: Factor the perfect square trinomial. ⎝p − 5⎠ = 18 Use the Square Root Property.
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Trajectories of fireworks are modeled by what kind of equations?
- Exponential equations
- Cubic equations
- Linear equations
- Quadratic equations
Reveal answer
Answer: Quadratic equations
Source evidence
PDF page 1163: The trajectories of fireworks are modeled by quadratic equations. The equations can be used to predict the maximum height of a firework and the number of seconds it will take from launch to explosion. In this chapter, we will study the properties of quadratic equations, solve them, graph them, and see how they are applied as models of various situations.
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In Example 10.1, solving x² = 169 begins by applying which property?
- Zero Product Property
- Distributive Property
- Square Root Property
- Factoring
Reveal answer
Answer: Square Root Property
Source evidence
PDF page 1165: EXAMPLE 10.1 2 Solve: x = 169 . Solution 2 x = 169 Use the Square Root Property.
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Why can't the equation x² = 7 be solved by factoring?
- 7 equals zero
- 7 is a perfect square
- 7 is negative
- 7 is not a perfect square
Reveal answer
Answer: 7 is not a perfect square
Source evidence
PDF page 1164: 2 2 We can easily use factoring to find the solutions of similar equations, like x = 16 and x = 25 , because 16 and 25 are 2 perfect squares. But what happens when we have an equation like x = 7 ? Since 7 is not a perfect square, we cannot solve the equation by factoring. 2 These equations are all of the form x = k . We defined the square root of a number in this way: 2
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When solving q² = −24 with the Square Root Property, the result is:
- Two positive solutions
- One solution only
- Zero as the solution
- No real solution
Reveal answer
Answer: No real solution
Source evidence
PDF page 1167: The −24 is not a real number. There is no real solution.
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To solve 5m² = 80 with the Square Root Property, you must first:
- Multiply both sides by 5
- Subtract 80 from both sides
- Divide both sides by 5
- Add 5 to both sides
Reveal answer
Answer: Divide both sides by 5
Source evidence
PDF page 1166: 5m 80 = Divide by 5 to make its cofficient 1. 5 5
PDF page 1166: To use the Square Root Property, the coefficient of the variable term must equal 1. In the next example, we must divide both sides of the equation by 5 before using the Square Root Property.
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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