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Write a Quadratic Equation Given the Vertex and Another Point>
Write a Quadratic Equation Given the Vertex and Another PointWrite a Quadratic Equation Given the Vertex and Another Point
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Question 1 of 2
1. Question
Find the equation of the graph belowHint
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Vertex Form
$$y=a{(x\color{#007DDC}{h})}^2+\color{#e65021}{k}$$where `(``h``,``k``)` is the vertexSince the graph indicates the vertex, use the Vertex Form. Slot `(``h``,``k``)` and `(x,y)` into the Vertex Form to solve for `a`. Then, substitute `a`, `h` and `k` back to the main formula to form an equation.First, label values from the graphNote that the vertex is at `(2,3)``h` `=` `2` from vertex `k` `=` `3` from vertex `x` `=` `5` `x` intercept `y` `=` `0` value of `y` at `x` intercept Now, slot these values into the Vertex Form and solve for `a``y` `=` $$a{(\color{#00880A}{x}\color{#007DDC}{h})}^2+\color{#e65021}{k}$$ Vertex Form `0` `=` $$a{(\color{#00880A}{5}(\color{#007DDC}{2}))}^2+\color{#e65021}{3}$$ Substitute values `0` `=` `a(3)^2+3` `0` `=` `9a+3` `9a+3` `=` `0` `9a+3` `3` `=` `0` `3` Subtract `3` from both sides `9a``divide9` `=` `3``divide9` Divide both sides by `9` `a` `=` `3/9` `a` `=` `1/3` Simplify Finally, substitute `a`, `h` and `k` into the Vertex Form`y` `=` $$a{(x\color{#007DDC}{h})}^2+\color{#e65021}{k}$$ Vertex Form `y` `=` $$\frac{1}{3}{(x(\color{#007DDC}{2}))}^2+\color{#e65021}{3}$$ Substitute values `y` `=` `1/3 (x+2)^2+3` `y=1/3 (x+2)^2+3` 
Question 2 of 2
2. Question
Find the equation of the graph belowHint
Help VideoCorrect
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Incorrect
Vertex Form
$$y=a{(x\color{#007DDC}{h})}^2+\color{#e65021}{k}$$where `(``h``,``k``)` is the vertexSince the graph indicates the vertex, use the Vertex Form. Slot `(``h``,``k``)` and `(x,y)` into the Vertex Form to solve for `a`. Then, substitute `a`, `h` and `k` back to the main formula to form an equation.First, label values from the graph`h` `=` `3` from vertex `k` `=` `2` from vertex `x` `=` `4` from given point `y` `=` `1` from given point Now, slot these values into the Vertex Form and solve for `a``y` `=` $$a{(\color{#00880A}{x}\color{#007DDC}{h})}^2+\color{#e65021}{k}$$ Vertex Form `1` `=` $$a{(\color{#00880A}{4}\color{#007DDC}{3})}^2+\color{#e65021}{2}$$ Substitute values `1` `=` `a(1)^2+2` `1` `=` `a+2` `a+2` `=` `1` `a+2``2` `=` `1``2` Subtract `2` from both sides `a` `=` `1` Finally, substitute `a`, `h` and `k` into the Vertex Form`y` `=` $$a{(x\color{#007DDC}{h})}^2+\color{#e65021}{k}$$ Vertex Form `y` `=` $$1{(x\color{#007DDC}{3})}^2+\color{#e65021}{2}$$ Substitute values `y` `=` `(x3)^2+2` `y=(x3)^2+2`
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