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Graph Quadratic Functions by Completing the SquareGraph Quadratic Functions by Completing the Square
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Question 1 of 4
1. Question
Graph the function`y=x^210x+15`Hint
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Vertex Form
`y=a(xh)^2+k`where `(h,k)` is the vertexCompleting the square is done by producing a square of a binomial on the left side of the equal sign. This method is useful when no two rational numbers solve the equation.Plot the vertex and `x` intercepts, then connect the points to form a parabolaFirst, find the vertex and plot this on the graphStart by transforming the function into vertex form`y` `=` `x^210x+15` `y``15` `=` `x^210x+15``15` Subtract `15` from both sides `y15` `=` `x^210x` Take the coefficient of the `x` term, divide it by two and then square it.`y15` `=` `x^2``10``x` Coefficient of the `x` term `=` $$\frac{\color{#00880A}{10}}{2}$$ Divide it by `2` $$(5)^2$$ `=` `25` Square This number will make the right side a perfect square.Add and subtract `25` to the right side to keep the balance.`y15` `=` `x^210x` `y15` `=` `x^210x+``25````25` Add and subtract `25` Now, transform the right side into a square of a binomial, then leave `y` on the left side.`y15` `=` `(x5)(x5)25` `y15` `=` `(x5)^225` `y15``+15` `=` `(x5)^225``+15` `y` `=` `(x5)^210` The function is now in vertex formCompare the function to the general vertex form to get the vertex`y` `=` `a(xh)^2+k` `y` `=` `(x5)^210` `h` `=` `5` `k` `=` `10` This means that the vertex is at `(5,10)`Next, find the `x` intercepts by substituting `y=0`, then solving for `x``y` `=` `(x5)^210` `0` `=` `(x5)^210` Substitute `y=0` `0``+10` `=` `(x5)^210``+10` Add `10` to both sides `10` `=` `(x5)^2` `sqrt10` `=` `sqrt((x5)^2)` Take the square root of both sides `+sqrt10` `=` `x5` `x5` `=` `+sqrt10` `x5``+5` `=` `+sqrt10``+5` Add `5` to both sides `x` `=` `5+sqrt10` `x` `=` `8.162, 1.838` Mark these `2` points on the `x` axisFinally, connect the points to form a parabola 
Question 2 of 4
2. Question
Graph the function`y=2x^28x+2`Hint
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Vertex Form
`y=a(xh)^2+k`where `(h,k)` is the vertexCompleting the square is done by producing a square of a binomial on the left side of the equal sign. This method is useful when no two rational numbers solve the equation.Plot the vertex and `x` intercepts, then connect the points to form a parabolaFirst, find the vertex and plot this on the graphStart by transforming the function into vertex form`y` `=` `2x^28x+2` `y` `=` `2(x^2+4x1)` Factor out `2` Take the coefficient of the `x` term, divide it by two and then square it.`y` `=` `2(x^2+``4``x1)` Coefficient of the `x` term `=` $$\frac{\color{#00880A}{4}}{2}$$ Divide it by `2` $$(2)^2$$ `=` `4` Square This number will make the right side a perfect square.Add and subtract `4` to the grouping of `x` to keep the balance.`y` `=` `2(x^2+4x1)` `y` `=` `2(x^2+4x+``4````4``1)` Add and subtract `4` `y` `=` `2((x+2)^241)` `y` `=` `2((x+2)^25)` `y` `=` `2(x+2)^2+10` This is now in vertex formCompare the function to the general vertex form to get the vertex`y` `=` `a(xh)^2+k` `y` `=` `2(x+2)^2+10` `h` `=` `2` `k` `=` `10` This means that the vertex is at `(2,10)`Next, find the `x` intercepts by substituting `y=0`, then solving for `x``y` `=` `2(x+2)^2+10` `0` `=` `2(x+2)^2+10` Substitute `y=0` `0` `10` `=` `2(x+2)^2+10` `10` Subtract `10` from both sides `10` `=` `2(x+2)^2` `10``:(2)` `=` `2(x+2)^2``:(2)` Divide both sides by `2` `5` `=` `(x+2)^2` `(x+2)^2` `=` `5` `sqrt((x+2)^2)` `=` `sqrt5` Take the square root of both sides `x+2` `=` `+sqrt5` `x+2` `2` `=` `+sqrt5` `2` Subtract `2` from both sides `x` `=` `2+sqrt5` Mark these `2` points on the `x` axisFinally, connect the points to form a parabola 
Question 3 of 4
3. Question
By completing the square, which graph is correct for the equation: `y=x^28x+24`.Hint
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Completing the square is done by producing a square of a binomial on the left side of the equal sign. This method is useful when no two rational numbers solve the equation.Perform the process of completing the square on the given quadratic to convert into vertex form.`y` `=` `x^28x+24` `=` `(x^28x` `+ (8/2)^2` `)` `(8/2)^2` `+ 24` Complete the square `=` `(x^28x` `+16``)` `16` `+ 24` Simplify `=` `(x^28x` `+16``)+8` `y` `=` `(x4)^2+8` Rewrite as a square of a binomial Identify the vertex of the graph from the given formula.`y` `=` $$a(x\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `(x4)^2+8` Given equation `y` `=` $$a(x\color{blue}{4})^2+\color{blue}{8}$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{4},\color{blue}{8})$$ Mark the vertex on the graph.Next, solve for the `y`intercept by substituting `x=0`.`y` `=` `(x4)^2+8` `y` `=` `(04)^2+8` Substitute `x=0` `y` `=` `16+8` `y` `=` `24` Mark the `y`intercept on the graph.Draw a parabola using the points. 
Question 4 of 4
4. Question
By completing the square, which graph is correct for the equation: `y=x^28x+18`.Hint
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Completing the square is done by producing a square of a binomial on the left side of the equal sign. This method is useful when no two rational numbers solve the equation.Perform the process of completing the square on the given quadratic to convert into vertex form.`y` `=` `x^28x+18` `=` `(x^28x` `+ (8/2)^2` `)` `(8/2)^2` `+ 18` Complete the square `=` `(x^28x` `+16``)` `16` `+ 18` Simplify `=` `(x^28x` `+16``)+2` `y` `=` `(x4)^2+2` Rewrite as a square of a binomial Identify the vertex of the graph from the given formula.`y` `=` $$a(x\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `(x4)^2+2` Given equation `y` `=` $$a(x\color{blue}{4})^2+\color{blue}{2}$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{4},\color{blue}{2})$$ Mark the vertex on the graph.Next, solve for the `y`intercept by substituting `x=0`.`y` `=` `(x4)^2+2` `y` `=` `(04)^2+2` Substitute `x=0` `y` `=` `16+2` `y` `=` `18` Mark the `y`intercept on the graph.Draw a parabola using the points.
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