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faust18 [17]
3 years ago
7

Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2)

. If necessary, round to the nearest hundredth. ​

Mathematics
1 answer:
lesya692 [45]3 years ago
4 0

Answer:

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Step-by-step explanation:

we know that

The equation of the given parabola is

(y-k)=a(x-h)^{2}

we have

the vertex is the point (5,-4)

substitute

(y+4)=a(x-5)^{2}

The y-intercept is the point (0,96)

substitute and solve for a

(96+4)=a(0-5)^{2}

100=a(25)

a=100/25=4

The equation of the vertical parabola is equal to

(y+4)=4(x-5)^{2}

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

4=4(x-5)^{2}

Simplify

1=(x-5)^{2}

Rewrite

(x-5)^{2}=1

square root both sides

(x-5)=(+/-)1

x=(+/-)1+5

x=(+)1+5=6

x=(-)1+5=4

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

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What is the peremeter of this polygon? (With picture)
lyudmila [28]
Check the picture below.

so.. simply, use the distance formula, to get their length an add them up, and that's the perimeter of the polygon.


\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -1}}\quad ,&{{ 2}})\quad 
%  (c,d)
&({{ 2}}\quad ,&{{ 4}})\\
&({{ 2}}\quad ,&{{ 4}})\quad 
%  (c,d)
&({{ 3}}\quad ,&{{ -2}})\\
&({{ 3}}\quad ,&{{ -2}})\quad 
%  (c,d)
&({{ -2}}\quad ,&{{ -3}})\\
&({{ -2}}\quad ,&{{ -3}})\quad 
%  (c,d)
&({{ -1}}\quad ,&{{ 2}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}

\bf -------------------------------\\\\
d=\sqrt{[2-(-1)]^2+(4-2)^2}\implies d=\sqrt{(2+1)^2+(2)^2}
\\\\\\
d=\sqrt{3^2+2^2}\implies \boxed{d=\sqrt{13}}\\\\
-------------------------------\\\\
d=\sqrt{(3-2)^2+(-2-4)^2}\implies d=\sqrt{1^2+(-6)^2}\implies \boxed{d=\sqrt{37}}\\\\
-------------------------------\\\\
d=\sqrt{(-2-3)^2+[-3-(-2)]^2}\implies d=\sqrt{(-5)^2+(-3+2)^2}
\\\\\\
d=\sqrt{(-5)^2+(-1)^2}\implies \boxed{d=\sqrt{26}}

\\\\
-------------------------------\\\\
d=\sqrt{[-1-(-2)]^2+[2-(-3)]^2}\implies d=\sqrt{(-1+2)^2+(2+3)^2}
\\\\\\
d=\sqrt{(1)^2+(5)^2}\implies \boxed{d=\sqrt{26}}

so, those are their lengths, sum them all up, that's the polygon's perimeter.

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Neporo4naja [7]
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ITS URGENT PLEASE HELP!!! I will give brainliest if correct! Someone please help?
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2) Commutative Property of Addition (we rearrange them):

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