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Intro to Quadratic Functions (Parabolas)>
Intro to Quadratic Functions (Parabolas) 2Intro to Quadratic Functions (Parabolas) 2
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Question 1 of 5
1. Question
Which of the following shows the graph of `y=x^2+3`?Hint
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The Basic Form of a Parabola
`y=``a``x^2+``C`Vertex: `(0,``C``)`First, identify the vertex of the parabola from the equation.`y` `=` `a``x^2+``C` `y` `=` `(``1``)x^2+``3` Highlight values of `a` and `C` `a` `=` `1` `C` `=` `3` Vertex is at `(0,``C``)`, so the graph’s vertex is at `(0,``3``)`.Plot the vertex on the graph.
Because the value of `a` is positive, the parabola is concave up. Draw a parabola from the vertex.
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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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The Basic Form of a Parabola
`y=``a``x^2+``C`Vertex: `(0,``C``)`First, identify the vertex of the parabola from the equation.`y` `=` `a``x^2+``C` `y` `=` `x^2` `y` `=` `(``1``)x^2+``0` Highlight values of `a` and `C` `a` `=` `1` `C` `=` `0` Vertex is at `(0,``C``)`, so the graph’s vertex is at `(0,``0``)`.Plot the vertex on the graph.
Because the value of `a` is positive, the parabola is concave up. Draw a parabola from the vertex.
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Question 3 of 5
3. Question
Which of the following shows the graph of `y=x^2-4`?Correct
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The Basic Form of a Parabola
`y=``a``x^2+``C`Vertex: `(0,``C``)`First, identify the vertex of the parabola from the equation.`y` `=` `a``x^2+``C` `y` `=` `x^2` `y` `=` `(``1``)x^2+(``-4``)` Highlight values of `a` and `C` `a` `=` `1` `C` `=` `-4` Vertex is at `(0,``C``)`, so the graph’s vertex is at `(0,``-4``)`.Plot the vertex on the graph.
Because the value of `a` is positive, the parabola is concave up. Draw a parabola from the vertex.
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Question 4 of 5
4. Question
Which of the following shows the equation of the graph below?
Hint
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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.A point on the parabola is `(``2`,`20``)`.Substitute the values of `x` and `y` into the equation for parabola.`y` `=` $$a\color{green}{x}^{2}$$ Equation of the parabola `20` `=` $$a(\color{green}{2})^{2}$$ `x=2` and `y=20` `20` `=` `4a` Simplify `5` `=` `a` Divide both sides by `4` `a` `=` `5` Substitute the value of `a` back to the equation.`y` `=` $$a\color{green}{x}^{2}$$ Equation of the parabola `y` `=` $$5\color{green}{x}^{2}$$ `a=5` `y` `=` `5x^2` `y=5x^2` -
Question 5 of 5
5. Question
Which of the following shows the equation of the graph below?
Hint
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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.A point on the parabola is `(``-3`,`-3``)`.Substitute the values of `x` and `y` into the equation for parabola.`y` `=` $$a\color{green}{x}^{2}$$ Equation of the parabola `-3` `=` $$a(\color{green}{-3})^{2}$$ `x=-3` and `y=-3` `-3` `=` `9a` Simplify `-1/3` `=` `a` Divide both sides by `9` `a` `=` `-1/3` Substitute the value of `a` back to the equation.`y` `=` $$a\color{green}{x}^{2}$$ Equation of the parabola `y` `=` $$-\frac{1}{3} \color{green}{x}^{2}$$ `a=-1/3` `y` `=` `-1/3x^2` `y=-1/3x^2`
Quizzes
- Solve Quadratics by Factoring
- 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
- Combining Methods for Solving Quadratic Equations