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Intro to Quadratic Functions (Parabolas)>
Intro to Quadratic Functions (Parabolas) 1Intro to Quadratic Functions (Parabolas) 1
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Question 1 of 5
1. Question
Which of the following shows the graph of `y=3x^2`?Hint
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Great Work!
Incorrect
If `a>0`, the parabola is concave up.
If `a<0`, the parabola is concave down.
A big `a` means a narrow parabola while a small `a` means it is wide.First, check the coefficient of the equation `y=``3``x^2`.The value of `a` is large, so we can deduce that the graph is narrow.Next, check the sign of `a`.Because `a=3` is positive, we can say that the graph is concave up.Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
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Question 2 of 5
2. Question
Which of the following shows the graph of `y=-x^2`?Hint
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Correct!
Incorrect
If `a>0`, the parabola is concave up.
If `a<0`, the parabola is concave down.
A big `a` means a narrow parabola while a small `a` means it is wide.First, check the coefficient of the equation `y=``-``x^2`.The value of `a` is `-1`, so we can deduce that the graph is of normal size.Next, check the sign of `a`.Because `a=-1` is negative, we can say that the graph is concave down.Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
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Question 3 of 5
3. Question
Which of the following shows the graph of `y=1/2x^2`?Hint
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Keep Going!
Incorrect
If `a>0`, the parabola is concave up.
If `a<0`, the parabola is concave down.
A big `a` means a narrow parabola while a small `a` means it is wide.First, check the coefficient of the equation `y=``1/2``x^2`.The value of `a` is small, so we can deduce that the graph is wide.Next, check the sign of `a`.Because `a=1/2` is positive, we can say that the graph is concave up.Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
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Question 4 of 5
4. Question
Which of the following shows the graph of `y=-4x^2`?Hint
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Fantastic!
Incorrect
If `a>0`, the parabola is concave up.
If `a<0`, the parabola is concave down.
A big `a` means a narrow parabola while a small `a` means it is wide.First, check the coefficient of the equation `y=``-4``x^2`.The value of `a` is a large negative number, so we can deduce that the graph is narrow.Next, check the sign of `a`.Because `a=-4` is negative, we can say that the graph is concave down.Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
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Question 5 of 5
5. Question
Which of the following shows the graph of `y=-1/4x^2`?Hint
Help VideoCorrect
Excellent!
Incorrect
If `a>0`, the parabola is concave up.
If `a<0`, the parabola is concave down.
A big `a` means a narrow parabola while a small `a` means it is wide.First, check the coefficient of the equation `y=``-1/4``x^2`.The value of `a` is a small negative number, so we can deduce that the graph is wide.Next, check the sign of `a`.Because `a=-1/4` is negative, we can say that the graph is concave down.Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
Quizzes
- Sum & Product of Roots 1
- Sum & Product of Roots 2
- Sum & Product of Roots 3
- Sum & Product of Roots 4
- Solving Equations by Factoring 1
- Solving Equations Using the Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Solving Reducible Equations