Solve Applications Modeled by Quadratic Equations Quiz
The question sheet
Reveal any answer as you study-
In a right triangle with legs a and b and hypotenuse c, what does the Pythagorean Theorem state?
- a² + b² = c²
- ab = c²
- a² − b² = c²
- a + b = c
Reveal answer
Answer: a² + b² = c²
Source evidence
PDF page 1242: • Pythagorean Theorem In any right triangle, where a and b are the lengths of the legs, and c is the length of
PDF page 1242: 2 2 2 the hypothenuse, a + b = c
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In the Pythagorean Theorem, c represents the length of the:
- hypotenuse
- shorter leg
- longer leg
- base
Reveal answer
Answer: hypotenuse
Source evidence
PDF page 1242: • Pythagorean Theorem In any right triangle, where a and b are the lengths of the legs, and c is the length of
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The projectile motion formula models the height in feet of an object shot upward with what quantity?
- gravity only
- initial velocity v
- constant force
- final velocity
Reveal answer
Answer: initial velocity v
Source evidence
PDF page 1242: • Projectile motion The height in feet, h , of an object shot upwards into the air with initial velocity, v , after t
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The graph of every quadratic equation is what shape?
- a circle
- a hyperbola
- a line
- a parabola
Reveal answer
Answer: a parabola
Source evidence
PDF page 1243: • The graph of every quadratic equation is a parabola.
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For y = ax² + bx + c, if a > 0, the parabola opens:
- downward
- upward
- right
- left
Reveal answer
Answer: upward
Source evidence
PDF page 1243: • Parabola Orientation For the quadratic equation y = ax + bx + c , if
PDF page 1243: ◦ a > 0 , the parabola opens upward.
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To find the y-coordinate of the vertex, you substitute the vertex's x-value into:
- the x-intercepts
- the quadratic equation
- the y-intercept
- the axis of symmetry
Reveal answer
Answer: the quadratic equation
Source evidence
PDF page 1243: ◦ To find the y-coordinate of the vertex we substitute x = −
PDF page 1243: into the quadratic equation.
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To find the y-intercept of a parabola, you:
- Let y = 0 and solve for x
- Set a = 0
- Let x = 1
- Let x = 0 and solve for y
Reveal answer
Answer: Let x = 0 and solve for y
Source evidence
PDF page 1243: y-intercept x-intercepts
PDF page 1243: Let x = 0 and solve for y. Let y = 0 and solve for x.
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To find the x-intercepts of a parabola, you:
- Let y = 1
- Set c = 0
- Let x = 0 and solve for y
- Let y = 0 and solve for x
Reveal answer
Answer: Let y = 0 and solve for x
Source evidence
PDF page 1243: y-intercept x-intercepts
PDF page 1243: Let x = 0 and solve for y. Let y = 0 and solve for x.
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In graphing a quadratic equation, what is Step 1?
- Write it with y on one side
- Find the x-intercepts
- Graph the parabola
- Find the vertex
Reveal answer
Answer: Write it with y on one side
Source evidence
PDF page 1243: Step 1. Write the quadratic equation with y on one side. Step 2. Determine whether the parabola opens upward or downward. Step 3. Find the axis of symmetry. Step 4. Find the vertex. Step 5. Find the y-intercept. Find the point symmetric to the y-intercept across the axis of symmetry. Step 6. Find the x-intercepts. Step 7. Graph the parabola.
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When graphing a quadratic equation, finding the axis of symmetry is which step?
- Step 5
- Step 2
- Step 3
- Step 7
Reveal answer
Answer: Step 3
Source evidence
PDF page 1243: Step 1. Write the quadratic equation with y on one side. Step 2. Determine whether the parabola opens upward or downward. Step 3. Find the axis of symmetry. Step 4. Find the vertex. Step 5. Find the y-intercept. Find the point symmetric to the y-intercept across the axis of symmetry. Step 6. Find the x-intercepts. Step 7. Graph the parabola.
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The y-coordinate of the vertex is the minimum value when the parabola:
- opens left
- is a line
- opens downward
- opens upward
Reveal answer
Answer: opens upward
Source evidence
PDF page 1243: ◦ The y-coordinate of the vertex of the graph of a quadratic equation is the
PDF page 1243: ◦ minimum value of the quadratic equation if the parabola opens upward.
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Section 10.1 covers solving quadratic equations using which property?
- Zero Product Property
- Square Root Property
- Distributive Property
- Addition Property
Reveal answer
Answer: Square Root Property
Source evidence
PDF page 1243: 10.1 10.1 Solve Quadratic Equations 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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