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3 years ago

what are the steps required to determine the equation of a quadratic function given its zeros and a point?

Mathematics

1 answer:

mezya [45]3 years ago

8 0

Answer:

Below

Step-by-step explanation:

The quadratic equations form is:

● ax^2+bx+c

Using the zeroes, we can write a factored form.

● a (x-x') (x-x")

x and x' are the zeroes

■■■■■■■■■■■■■■■■■■■■■■■■■■

●y = a (x-x') (x-x")

x' and x" are khown but a is not.

We are given a point so replace x and y with its coordinates to find a.

So the steps are:

● 1) Write the factored form of the quadratic equation

● 2) replace x' and x" with their values.

● 3) replace x and y with the coordinates of a khwon point.

● 4) solve the equation for a.

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50 POINTS!!!

san4es73 [151]

Step-by-step explanation:

<u>Step 1: Determine an ordered pair</u>

A solution of an equation just means that the point lies on the line. We can find any y-value when we plug in a specific x-value. For example, if we want to know what ordered pair lies at x=1, we just plug in y = -1/2(1) and solve for y which gives us -1/2. This gives us an ordered pair of (1, -1/2). We can continue to do this for any x value.

We can also reverse the order and plug in the y-value and get the x-value in order to accomplish the same goal but it's a bit harder.

Hope this helps!

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2 years ago

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Find the area of the rectangle with a length of (x^2-2) and a width of (2x^2-x+2)

Katyanochek1 [597]

Area=legnth times width

so multiply them together use distributive property
a(b+c)=ab+ac so
in this problem
(a+b)(c+d+e)=(a+b)(c)+(a+b)(d)+(a+b)(e)

so
x^2-2 times (2x^2-x+2)=(x^2)(2x^2-x+2)-(2)(2x^2-x+2)=(2x^4-x^3+2x^2)-(4x^2-2x+4)
add like terms
2x^4-x^3+(2x^2-4x^2)-2x+4
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3 years ago

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When Justin goes to work, he drives at an average speed of 65 miles per hour. It takes about 1 hour and 30 minutes for Justin to

Fofino [41]

Answer:

Justin spends $14.24 on gas to travel to work.

Step-by-step explanation:

Given:

Average speed at which Justin goes to work = 65 miles/hour

Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]

Distance he can travel per gallon of gas = 25 miles.

Cost of per gallon of gas = $3.65

Solution:

We first determine the distance Justin travels to work.

Distance = $Speed\times time$

Distance = $65\times 1.5 = 97.5\ miles$

Using unitary method to find the amount of gas required to cover the distance.

If 25 miles is covered in 1 gallon of gas

Then 1 mile will be covered in = $\frac{1}{25}$ gallons of gas

So, to cover 97.5 miles gas required = $\frac{1}{25}\times 97.5=3.9$ gallons of gas.

Using unitary method to find the cost of 3.9 gallons of gas.

Cost of 1 gallon of gas = $3.65

So, cost of 3.9 gallons of gas will be = $\$3.65\times 3.9=\$14.235\approx\$14.24$ (Answer)

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4 years ago

Which of the following has a solution set of {x | x = 0}?

notka56 [123]

Answer:

(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}

Step-by-step explanation:

Here, the given expression is : {x | x = 0}

So, the ONLY element in the given set = {0}

Now, take each option and solve the given expression:

(a) x + 1 < -1

Adding -1 BOTH sides, we get:

x + 1 -1 < -1 -1

or, x < - 2 ⇒ x = { -∞ , .... , -4,-3}

Also, x + 1 < 1

Adding -1 BOTH sides, we get:

x + 1 -1 < 1 -1

or, x <0 ⇒ x = { -∞ , .... , -4,-3,-2,-1}

So, (x + 1 < -1) ∩ (x + 1 < 1) = { -∞ , .... , -4,-3}∩ { -∞ , .... , -4,-3,-2,-1}

= { -∞ , .... , -4,-3}

⇒ (x + 1 < -1) ∩ (x + 1 < 1) ≠ {0}

Similarly, solving

(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1)

(x + 1 ≤ 1) = x≤ 0 = { -∞ , .... , -4,-3,-2,-1, 0}

(x + 1 ≥ 1) = x ≥ 0 = {0,1,2,3,... ∞}

⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {0}

(b)(x + 1 < 1) ∩ (x + 1 > 1)

(x + 1 < 1) = x < 0 = { -∞ , .... , -4,-3,-2,-1}

(x + 1 > 1) = x > 0 = { 1,2,3,... ∞}

⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = Ф

Hence, (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}

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4 years ago

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The cost of grapes was $0.88 a pound. Change bought 4.5 pounds. Find the amount he paid.

Schach [20]

Answer:

$3.96

Step-by-step explanation:

If he gave $.88 per each pound he bought all you have to do is multiply $.88 by how many pounds he bought 4.5. $.88x4.5 equals $3.96

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3 years ago

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what are the steps required to determine the equation of a quadratic function given its zeros and a point?​

what are the steps required to determine the equation of a quadratic function given its zeros and a point?