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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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