Graph -16x^2+264x

Math
-16×2+264x
Find the properties of the given parabola.
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Rewrite the equation in vertex form.
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Complete the square for -16×2+264x.
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Use the form ax2+bx+c, to find the values of a, b, and c.
a=-16,b=264,c=0
Consider the vertex form of a parabola.
a(x+d)2+e
Substitute the values of a and b into the formula d=b2a.
d=2642(-16)
Simplify the right side.
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Cancel the common factor of 264 and 2.
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Factor 2 out of 264.
d=2⋅1322⋅-16
Cancel the common factors.
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Factor 2 out of 2⋅-16.
d=2⋅1322(-16)
Cancel the common factor.
d=2⋅1322⋅-16
Rewrite the expression.
d=132-16
d=132-16
d=132-16
Cancel the common factor of 132 and -16.
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Factor 4 out of 132.
d=4(33)-16
Cancel the common factors.
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Factor 4 out of -16.
d=4⋅334⋅-4
Cancel the common factor.
d=4⋅334⋅-4
Rewrite the expression.
d=33-4
d=33-4
d=33-4
Move the negative in front of the fraction.
d=-334
d=-334
Find the value of e using the formula e=c-b24a.
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Simplify each term.
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Raise 264 to the power of 2.
e=0-696964⋅-16
Multiply 4 by -16.
e=0-69696-64
Divide 69696 by -64.
e=0+1089
Multiply -1 by -1089.
e=0+1089
e=0+1089
Add 0 and 1089.
e=1089
e=1089
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
-16(x-334)2+1089
-16(x-334)2+1089
Set y equal to the new right side.
y=-16(x-334)2+1089
y=-16(x-334)2+1089
Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=-16
h=334
k=1089
Since the value of a is negative, the parabola opens down.
Opens Down
Find the vertex (h,k).
(334,1089)
Find p, the distance from the vertex to the focus.
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Find the distance from the vertex to a focus of the parabola by using the following formula.
14a
Substitute the value of a into the formula.
14⋅-16
Simplify.
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Multiply 4 by -16.
1-64
Move the negative in front of the fraction.
-164
-164
-164
Find the focus.
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The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.
(h,k+p)
Substitute the known values of h, p, and k into the formula and simplify.
(334,6969564)
(334,6969564)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=334
Find the directrix.
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The directrix of a parabola is the horizontal line found by subtracting p from the y-coordinate k of the vertex if the parabola opens up or down.
y=k-p
Substitute the known values of p and k into the formula and simplify.
y=6969764
y=6969764
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Down
Vertex: (334,1089)
Focus: (334,6969564)
Axis of Symmetry: x=334
Directrix: y=6969764
Direction: Opens Down
Vertex: (334,1089)
Focus: (334,6969564)
Axis of Symmetry: x=334
Directrix: y=6969764
Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.
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Replace the variable x with 7 in the expression.
f(7)=-16(7)2+264(7)
Simplify the result.
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Simplify each term.
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Raise 7 to the power of 2.
f(7)=-16⋅49+264(7)
Multiply -16 by 49.
f(7)=-784+264(7)
Multiply 264 by 7.
f(7)=-784+1848
f(7)=-784+1848
Add -784 and 1848.
f(7)=1064
The final answer is 1064.
1064
1064
The y value at x=7 is 1064.
y=1064
Replace the variable x with 9 in the expression.
f(9)=-16(9)2+264(9)
Simplify the result.
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Simplify each term.
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Raise 9 to the power of 2.
f(9)=-16⋅81+264(9)
Multiply -16 by 81.
f(9)=-1296+264(9)
Multiply 264 by 9.
f(9)=-1296+2376
f(9)=-1296+2376
Add -1296 and 2376.
f(9)=1080
The final answer is 1080.
1080
1080
The y value at x=9 is 1080.
y=1080
Graph the parabola using its properties and the selected points.
xy71064334108991080
xy71064334108991080
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex: (334,1089)
Focus: (334,6969564)
Axis of Symmetry: x=334
Directrix: y=6969764
xy71064334108991080
Graph -16x^2+264x

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