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3 years ago

A parabola has an x-intercept of -1, a y-intercept of -3, and a minimum of -4 at x = 1.

Mathematics

1 answer:

torisob [31]3 years ago

4 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(1,-4)

substitute

$y=a(x-1)^{2}-4$

we have

An x-intercept of (-1,0)

substitute and solve for a

$0=a(-1-1)^{2}-4$

$0=4a-4$

$4a=4$

$a=1$

The equation is

$y=(x-1)^{2}-4$

<u><em>Verify the y-intercept</em></u>

For x=0

$y=(0-1)^{2}-4$

$y=-3$

The y-intercept is the point (0,-3) -----> is correct

using a graphing tool

see the attached figure

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The daily profit P (in thousands of dollars) from the sale of televisions is a function of the number x of televisions sold (

scZoUnD [109]

Answer:

The break-even sales amounts is 36 or 224.

Step-by-step explanation:

Consider the provided function.

$P= -5x^2 + 13x - 4$

Where x is the number of televisions sold (in hundreds) and P is the profit.

We need to calculate the break-even sales amounts.

the break-even sales amounts is the sales amounts that result in no profit or loss.

That means substitute P=0 and solve for x.

$-5x^2 + 13x - 4=0$

$5x^2-13x+4=0$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute a=4, b=-13 and c=4 in above formula.

$x_{1,\:2}=\frac{-\left(-13\right)\pm \sqrt{\left(-13\right)^2-4\cdot \:5\cdot \:4}}{2\cdot \:5}$

$x_{1,\:2}=\frac{13\pm\sqrt{169-80}}{10}$

$x_{1,\:2}=\frac{13\pm\sqrt{89}}{10}$

$x=\frac{13+\sqrt{89}}{10},\:x=\frac{13-\sqrt{89}}{10}\\x\approx2.243, \ or\ x\approx 0.357$

Therefore, the break-even sales amounts is 36 or 224.

7 0

3 years ago

Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day

AfilCa [17]

Answer:

Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = $5\frac34 \ hrs.$

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

$5\frac34 \ hrs.$ can be Rewritten as $\frac{23}{4}\ hrs$

Number of hours rode on first day = $\frac{23}{4}\ hrs$

Also Given:

Number of hours rode on second day = $6\frac45 \ hrs$

$6\frac45 \ hrs$ can be Rewritten as $\frac{34}{5}\ hrs.$

Number of hours rode on second day = $\frac{34}{5}\ hrs.$

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = $20-\frac{23}{4}-\frac{34}{5}$

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = $\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}$