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Slav-nsk [51]
3 years ago
7

Write the standard form of the quadratic equation modeled by the points shown in the table below.

Mathematics
2 answers:
Andre45 [30]3 years ago
6 0
We know that

The Standard Form<span> of a </span>Quadratic Equation<span> is
</span> ax²<span> + bx + c = 0
</span>
then 
for x=0    y=-6
 a*0² + b*0 + c = -6---------> c=-6

for x=1    y=2
 a*1² + b*1 -6 = 2---------> a+b=8---------> a=8-b---------> equation 1

for x=3    y=-0
 a*3² + b*3 -6 = 0---------> 9a+3b=6---------> equation 2

<span>substituting 1 in 2
9*(8-b)+3b=6------> 72-9b+3b=6---------> 6b=66--------> b=11
a=8-11-------> a=-3
so
a=-3
b=11
c=-6
</span>Standard Form of a Quadratic Equation is
 -3x² + 11x - 6 = 0
<span>
the answer is
</span> -3x² + 11x - 6 = 0<span>

</span>
Anton [14]3 years ago
3 0

Answer:

The required equation is -3x^2+11x-6

Step-by-step explanation:

Consider the provided table.

As we know the standard form of the quadratic equation is y=ax^2+bx+c

Substitute x=0 and y=-6 in above standard equation.

-6=a(0)^2+b(0)+c

-6=c

Substitute x=1, y=2 and c=-6 in standard equation.

2=a(1)^2+b(1)-6

2=a+b-6

a+b=8

a=8-b

Substitute x=2, y=4 and c=-6 in standard equation.

4=a(2)^2+b(2)-6

4=4a+2b-6

4a+2b=10

2a+b=5

Substitute value of a in above equation.

2(8-b)+b=5

16-2b+b=5

b=11

Substitute the value of b in a=8-b

a=8-11

a=-3

Hence, the required equation is -3x^2+11x-6

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