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Intro to Quadratic Functions (Parabolas)>
Intro to Quadratic Functions (Parabolas) 3Intro to Quadratic Functions (Parabolas) 3
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Question 1 of 5
1. Question
Which of the following shows the graph of `y=-x^2+5`?Correct
Well Done!
Incorrect
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+5` `y` `=` `(``-1``)x^2+``5` Highlight values of `a` and `C` `a` `=` `-1` `C` `=` `5` Vertex is at `(0,``C``)`, so the graph’s vertex is at `(0,``5``)`.Plot the vertex on the graph.
Because the value of `a` is negative, the parabola is concave down. 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`?Correct
Excellent!
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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 negative, the parabola is concave down. 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^2-2`?Correct
Keep Going!
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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^2-2` `y` `=` `(``-1``)x^2+(``-2``)` Highlight values of `a` and `C` `a` `=` `-1` `C` `=` `-2` Vertex is at `(0,``C``)`, so the graph’s vertex is at `(0,``-2``)`.Plot the vertex on the graph.
Because the value of `a` is negative, the parabola is concave down. 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
Help VideoCorrect
Great Work
Incorrect
The Basic Form of a Parabola
`y=``a``x^2+``C`Vertex: `(0,``C``)`Solve for `C` using the `y`-intercept of the graph. The `y`-intercept is `(0,-3)`.`y` `=` `ax^2+C` Equation of the parabola `-3` `=` `a(0)^2+C` `x=0` and `y=-3` `-3` `=` `C` Simplify `C` `=` `-3` A point on the parabola is `(``2`,`5``)`.Substitute the values of `x` and `y` into the equation for parabola together with the value of `C` to solve for `a`.`y` `=` $$\color {#e11584}{a}\color{green}{x}^{2}+C$$ Equation of the parabola `5` `=` $$\color{#e11584}{a}(\color{green}{2})^{2}+(-3)$$ `x=2`, `y=5` and `C=-3` `5` `=` `4a-3` Simplify `8` `=` `4a` Add `3` to both sides `2` `=` `a` Divide both sides by `4` `a` `=` `2` Substitute the value of `a` back to the equation.`y` `=` $$\color{#e11584}{a}\color{green}{x}^{2}+C$$ Equation of the parabola `y` `=` $$\color{#e11584}{2}\color{green}{x}^{2}-3$$ `a=2` and `C=-3` `y` `=` `2x^2-3` `y=2x^2-3` -
Question 5 of 5
5. Question
Which of the following shows the equation of the graph below?
Hint
Help VideoCorrect
Exceptional!
Incorrect
The Basic Form of a Parabola
`y=``a``x^2+``C`Vertex: `(0,``C``)`Solve for `C` using the `y`-intercept of the graph. The `y`-intercept is `(0,-1)`.`y` `=` `ax^2+C` Equation of the parabola `-1` `=` `a(0)^2+C` `x=0` and `y=-1` `-1` `=` `C` Simplify `C` `=` `-1` A point on the parabola is `(``-2`,`-3``)`.Substitute the values of `x` and `y` into the equation for parabola together with the value of `C` to solve for `a`.`y` `=` $$\color {#e11584}{a}\color{green}{x}^{2}+C$$ Equation of the parabola `-3` `=` $$\color{#e11584}{a}(\color{green}{-2})^{2}+(-1)$$ `x=2`, `y=5` and `C=-3` `-3` `=` `4a-1` Simplify `-2` `=` `4a` Add `1` to both sides `-1/2` `=` `a` Divide both sides by `4` `a` `=` `-1/2` Substitute the value of `a` back to the equation.`y` `=` $$\color{#e11584}{a}\color{green}{x}^{2}+C$$ Equation of the parabola `y` `=` $$\color{#e11584}{-\frac{1}{2}}\color{green}{x}^{2}-1$$ `a=-1/2` and `C=-1` `y` `=` `-1/2x^2-1` `y=-1/2x^2-1`
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