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Graph Quadratic Functions in Standard Form 1Graph Quadratic Functions in Standard Form 1
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Question 1 of 4
1. Question
Graph `y=3x^2+6x`.Hint
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Standard Form of a Parabola
$$\color{green}{y}=a \color{green}{x}^{2}+b\color{green}{x}+c$$The value of `a` is positive, so the parabola is concave up. Solve for the `y`intercept by substituting `x=0` into the equation.`y` `=` $$3\color{green}{x}^{2}+6\color {green}{x}$$ `=` $$3 ( \color{green}{0}^{2})+6(\color {green}{0}) $$ Substitute `x=0` `y` `=` `0` Mark the `y`intercept on the graph.Next, solve for the `x`intercepts by substituting `y=0`.`y` `=` $$3\color{green}{x}^{2}+6\color {green}{x}$$ `0` `=` $$3\color{green}{x}^{2}+6\color {green}{x}$$ Substitute `y=0` `0` `=` `3x(x+2)` Factor out `3` `3x(x+2)` `=` `0` `3x` `=` `0` Equate factors to `0` `x` `=` `0` `x+2` `=` `0` Equate factors to `0` `x` `=` `2` Mark the `x`intercepts on the graph.Draw a parabola using the points. 
Question 2 of 4
2. Question
Graph `y=8x2x^2`.Hint
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Standard Form of a Parabola
$$\color{green}{y}=a \color{green}{x}^{2}+b\color{green}{x}+c$$Rewrite the equation so that it is in standard form.`y` `=` `8x2x^2` `y` `=` `2x^2+8x` The value of `a` is negative, so the graph is concave down.Find the `y`intercept of the equation by substituting `x=0`.`y` `=` $$2\color{green}{x}^{2}+8\color {green}{x}$$ `=` $$2 ( \color{green}{0}^{2})+8(\color {green}{0}) $$ Substitute `x=0` `y` `=` `0` Next, solve for the `x`intercepts by substituting `y=0`.`y` `=` $$2\color{green}{x}^{2}+8\color {green}{x}$$ `0` `=` $$2\color{green}{x}^{2}+8\color {green}{x}$$ Substitute `y=0` `0` `=` `2x(x4)` Factor out `2x` `2x(x4)` `=` `0` `2x` `=` `0` Equate factors to `0` `x` `=` `0` `x4` `=` `0` Equate factors to `0` `x` `=` `4` Mark the `x`intercepts on the graph.Find the vertex from the formula `x=b/(2a)``x` `=` `b/(2a)` `=` `8/(2(2))` `a=2`,`b=8` `=` `8/(4)` `x` `=` `2` Solve for the `y`intercept of the vertex using the obtained value of `x`.`y` `=` `2x^2+8x` `=` `2(2^2)+8(2)` `=` `2(4)+16` `=` `8+16` `y` `=` `8` Draw a parabola using the points, together with the obtained vertex `(2,8)` 
Question 3 of 4
3. Question
Graph `y=2x^24x+3`.Hint
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Standard Form of a Parabola
$$\color{green}{y}=a \color{green}{x}^{2}+b\color{green}{x}+c$$The value of `a` is positive, so the graph is concave up.Find the vertex of the parabola by first solving for `x` from the formula `x=b/(2a)`.`x` `=` `b/(2a)` `=` `(4)/(2(2))` `a=2`,`b=4` `=` `4/4` `x` `=` `1` Substitute the value of `x` into the quadratic equation.`y` `=` $$2\color{green}{x}^{2}4\color {green}{x}+3$$ `=` $$2(\color{green}{1}^{2})4(\color {green}{1})+3$$ Substitute `x=1` `=` `2(1)4+3` `=` `21` `y` `=` `1` Simplify This corresponds to a vertex of `(1,1)`. Mark this on the graph.Find the `y`intercept of the graph. This is equal to `c`, which is equal to `3`. Plot this on the graph as well.Connect the points and take note that the parabola opens up. 
Question 4 of 4
4. Question
Graph `y=x^2+4x+5`.Hint
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Standard Form of a Parabola
$$\color{green}{y}=a \color{green}{x}^{2}+b\color{green}{x}+c$$The value of `a` is negative, so the graph is concave down.Find the `y`intercept of the graph. This is equal to `c`, which is equal to `5`. Plot this on the graph.Find the `x`intercept of the graph by substituting `y=0`.`y` `=` `x^2+4x+5` `0` `=` `x^2+4x+5` `y=0` Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.```x^2+` `4``x+` `5``=0`To factorise, we need to find two numbers that add to `4` and multiply to `5`Read across to get the factors.`(x+5)(x+1)`Solve for the `x`intercepts and plot them on the graph.`x+5` `=` `0` Solve for `x` `x` `=` `5` `x+1` `=` `0` Solve for `x` `x` `=` `1` Connect the points and take note that the parabola opens up.
Quizzes
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 Intro to Quadratic Functions (Parabolas) 1
 Intro to Quadratic Functions (Parabolas) 2
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 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