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2 years ago

Help Me please Urgent Help 15 Points

Mathematics

1 answer:

Ludmilka [50]2 years ago

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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)

lesya692 [45]

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)

4 0

2 years ago

A car travels 365 miles on 8 gallons of gas and what is the Unit rate?

Yakvenalex [24]

It will be 45 over 1

5 0

2 years ago

Read 2 more answers

If g(x) = 4√x-8 , which statement is true?

Mariana [72]

We have the following function:

$g(x)=4\sqrt{x}-8$

So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:

First. The function is defined only for $x\geq 0$ as shown in the Figure. This is also true because of $\sqrt{x}$ where $x$ must be greater (or equal) than zero.

Second. The range of the function are the values of $y\geq -8$ .

Third. If $x$ creases then $y$ always creases, too.