Mathematics, 27.06.2019 01:30 borbin

Write the equation of the parabola in standard form that passes through the points (0, 3), (1, -4), and (-1, 4).

Answers: 2

Show answers

Answers

Answer from: darrenturner

Answer

y = -3x^2-4x+3

Explanation

The standard form of a parabola is

y = ax^2 + bx + c,

where $a \ne 0$ , and a,b,c are real numbers.

If it passes through (0,3) then when x = 0, y = 3 so this means that

$3 = a(0)^2 + b(0) + c \implies c = 3$

so y = ax^2 + bx + 3 .

If it passes through (1,-4), then when x = 1, y = -4 so

$\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}$

If it passes through (-1,4) then when x = -1, y = 4 so

$\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}$

Because both (I) and (II) need to be satisfied, we have the system of equations,

$\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}$

which we can easily solve by adding the two equations up to get

$\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}$

Then we take any of the previous equations to solve for b:

$\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}$

Thus the parabola in standard form is

y = -3x^2-4x+3.

Answer from: kmart4062

StepsStandard Form of a Parabola: y = ax² + bx + c (a ≠ 0)

So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:

$3=a*0^2+b*0+c\\3=c$

Now we know that the value of c is 3.

Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):

$-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b$

Next, plug (-1,4) into the standard form formula and simplify:

$4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b$

With the last two simplified equations, we will create a system of equations:

$-7=a+b\\1=a-b$

With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:

-6=2a

From here we can solve for a. For this, just divide both sides by 2:

-3=a

Now that we have the value of a, plug it into either equation to solve for b:

$-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b$

Answer

Now, plug the obtained values in our standard form equation and your final answer will be:

y=-3x^2-4x+3

Answer from: Quest

step-by-step explanation:

use context clues to figure out the meaning of the bolded word:

the sage gardener knew when she had to water her plants.

question 8 options:

mint plant

wise

happy

lazy

Answer from: Quest

sounds & other waves originate from any vibrating object

Another question on Mathematics

Mathematics, 21.06.2019 17:30

When the solutions to each of the two equations below are graphed in the xy-coordinate plane, the graphs of the solutions intersect at two places. write the y-cordninates of the points of intersection in the boxes below in order from smallest to largest. y=2x y=x^2-3

Answers: 1

Answer

Mathematics, 21.06.2019 18:40

Which of the following represents the range of the graph of f(x) below

Answers: 1

Answer

Mathematics, 22.06.2019 02:10

Overproduction of uric acid in the body can be an indication of cell breakdown. this may be an advance indication of illness such as gout, leukemia, or lymphoma.† over a period of months, an adult male patient has taken nine blood tests for uric acid. the mean concentration was x = 5.35 mg/dl. the distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl. (a) find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. what is the margin of error? (round your answers to two decimal places.) lower limit upper limit margin of error (b) what conditions are necessary for your calculations? (select all that apply.) σ is unknown n is large σ is known normal distribution of uric acid uniform distribution of uric acid (c) interpret your results in the context of this problem. there is not enough information to make an interpretation. the probability that this interval contains the true average uric acid level for this patient is 0.05. the probability that this interval contains the true average uric acid level for this patient is 0.95. there is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. there is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. (d) find the sample size necessary for a 95% confidence level with maximal margin of error e = 1.10 for the mean concentration of uric acid in this patient's blood. (round your answer up to the nearest whole number.) blood tests

Answers: 2

Answer

Mathematics, 22.06.2019 03:00

You’re ordering more thread for blue jeans co. you usually purchase from ted’s threads, which sells 12 thread spools for $27. you recently received a notice from wade's wares that says you can buy thread from them for $2.30 each for the first 2 dozen and $2 a spool thereafter. you need to order 5 dozen spools. what percentage can you save by going with wade’s wares?

Answers: 1

Answer

You know the right answer?

Write the equation of the parabola in standard form that passes through the points (0, 3), (1, -4),...

Questions

Mathematics, 11.10.2019 02:10

Write the following equation in slope-intercept form. 1/3 - y+6=0...

Mathematics, 11.10.2019 02:10

Write a story problem that can be solved by finding the difference of 432,906 and 61,827.then solve the problem...

Mathematics, 11.10.2019 02:10

The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. assuming that the world population f...