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mezya [45]
2 years ago
13

The solutions to a certain quadratic equation are x = -4 and x = 3. Write the equation in standard form below.

Mathematics
2 answers:
elena-14-01-66 [18.8K]2 years ago
5 0
y=a(x-x_1)(x-x_2)\\\\x_1=-4;\ x_2=3\ therefore\\\\y=a(x+4)(x-3)\\\\y=a(x^2+x-12)\\\\\boxed{y=ax^2+ax-12a}\ where\ a\in\mathbb{R}-\{0\}
Vaselesa [24]2 years ago
5 0

Answer:

y=x²+x-12

Step-by-step explanation:

The quadratic standard form is given by this formula: ax² +bx +c =0.

However all we have is the zeros of this function.

1) So let's start by plugging into x the zeros. We will have two linear functions

y=ax^{2} +bx+c\\\\ y=a(3)^{2} +3b+c\\ y=9a+3b+c \\ y=16a+4b+c

2) Solving the system of linear equations, by the Addition Method:

\left \{{{9a+3b+c=0} \atop {16a-4b+c=0}} \right.\\  \left \{{{9a+3b+c*(-1)=0} \atop {16a-4b+c=0}} \right\\ \left \{{{-9a-3b-c=0} \atop {16a-4b+c=0}} \right. \\ \\ 7a-7b=0\\ a=b\\ \\9+3+c=0\\ c=-12

Therefore a=b and c=-12 and x=-4 and x=3

Since a=b, let's assume a=1 and b=1 and as c=-12 is the product of -4*3 hence we can rewrite this equation grouping it, and then test it:

y=(x+4)(x-3)\\ y=x^{2} -3x+4x-12\\ y=x^{2} +x-12 Standard form

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Factor completely 6x^2 -4x
Liono4ka [1.6K]

Answer:

2x(3x−2)

Step-by-step explanation:

Factor 6x^{2} − 4x

6x^{2} − 4x

=2x(3x−2)

Hope this helps!

4 0
2 years ago
The fare for an Uber is $5 per trip plus $0.50 per mile. The fare for the trip from the airport to the school center was $11.50.
Vinvika [58]

Answer:

13 miles

Step-by-step explanation:

The fare for the Uber

Cost= 5+ .5 m  

where m is the number of miles

We spent 11.50

11.50 = 5 + .5 m

Subtract 5 from each side

11.5 -5 = 5+.5m -5

6.50 = .5 m

Divide by .5 on each side

6.5/.5 = .5m/.5

13 = m

We went 13 miles

6 0
3 years ago
Solve the system of equations.<br> y=7x<br> y=2x + 20<br><br> x=?<br> y=?
alekssr [168]
X=4, y=28. 7x=2x+20, so subtract 2x from both sides and you’ll get 5x=20. Divide both sides by 5 and you’ll get x=4. Substitute this into the other equations and they will both equal 28.
6 0
3 years ago
Select the locations on the number line to plot the points 11 /4 and 19 /4 .
KIM [24]

Answer:


Step-by-step explanation:


6 0
2 years ago
A ream of paper contains 500 sheets of paper. Norm has 373 sheets of paper left from a ream. Express the portion of a ream Norm
Lunna [17]

Answer: In fraction : \dfrac{373}{500}

In Decimal :  0.746

Step-by-step explanation:

Given : A ream of paper contains 500 sheets of paper.

Norm has 373 sheets of paper left from a ream.

Then, the fraction of ream Norm has will be :-

\dfrac{\text{Number of sheets left from ream }}{\text{Total sheets in a ream }}\\\\=\dfrac{373}{500}

To convert in decimal we divide 373 by 500, we get 0.746.

Hence, The portion of a ream Norm has as = \dfrac{373}{500} or 0.746

3 0
2 years ago
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