If P(x) = 2x^3 - ax^2 + 10 and P(-2) = 4, find P(3).?

Question

If P(x) = 2x^3 - ax^2 + 10 and P(-2) = 4, find P(3).

What is the value of a?
What is the value of P(3)?

Answer 1

P(x) = 2x^3 - ax^2 + 10

P(-2) = 2(-2)^3 - a(-2)^2 + 10

=> 4 = 2 * -8 - a * 4 +10

=> 4 = -16 -4a + 10

=> 4 = -6 - 4a

=> 4 + 6 = -4a

=> 10/-4 = a

=> a = -5/2 = -2.5




P(3) = 2(3)^3 - 2.5 * (3)^2 +10

= 2 * 27 - (-2.5) * 9 + 10

= 54 + 22.5 + 10

= 86.5


Therefore,
P(3) = 86.5 = 173/2

Answer 2

P(-2) is 4, so, if we substitute all x's with -2, the answer will be equal to 4. In this manner, we will be able to solve for the value of a. So,:

---> 2(-2)^3 - a(-2)^2 + 10 = 4
---> 2(-8) - 4a +10 = 4
---> -4a = 10
---> a = - 5/2 or - 2.5 or - 2 and a half ---> your value for a!

Now that we have a value for a, we can substitute it to the original equation. We now have function:

P(x) = 2x^3 + (5/2)x^2 + 10

Then, we get P(3):

P(3) = 2(3)^3 + (5/2)(3)^2 + 10
P(3) = 2(27) + (5/2)(9) + 10
P(3) = 54 + 22.5 + 10
P(3) = 86.5 or 86 and a half or 173/2

ANSWERS:
a = - 2.5
P(3) = 86.5

Answer 3

If P(x) = 2x^3 - ax^2 + 10 and P(-2) = 4, find P(3).

If P(x) = 2x^3 - ax^2 + 10 you can use P(-2) = 4 to solve for a

P(-2) = 4 means x is -2 and function value is equal to 4.

as you plug in

2*(-2)^3 - a*(-2)^2 + 10= 4

2*(-8) - a*4 + 10 = 4

-16 - 4*a + 10 = 4

combine number part and variable part on left side

-6 - 4*a = 4

-6 + 6 - 4*a = 4 + 6

-4*a = 10

a / (-4) = 10 / (-4)

a = -2.5

Now you know the whole function,
P(x) = 2x^3 + (2.5)x^2 + 10

And you want to know P(3) = ?

P(3) = 2*3^3 + (2.5)*3^2 + 10

= 2*27 + 2.5*9 + 10

= 54 + 22.5 + 10

= 86.5

Answer: a= 2.5; P(3)=86.5

*still confused? write back

Answer 4

P(-2) = 2*(-2)^3 - a*(-2)^2 + 10 = 4

-16 - 4a + 10 = 4

4a = -16 + 10 - 4 = -10

a = -2.5


P(3) = 2*(3)^3 + 2.5*(3)^2 + 10

= 54 + 22.5 + 10

= 86.5

Answer 5

P(-2) = 4

4 = 2(-2)³ - a(-2)² + 10
4 = -16 - 4a + 10
10 = -4a
so a = -2.5

P(3) = 2(3)³ - (-2.5)(3)² + 10
P(3) = 2(27) - (-2.5)(9) + 10
P(3) = 54 + 22.5 + 10
P(3) = 86.5

Answer 6

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Answer 7

2(-2)^3-a(-2)^2+10=4
-16-4a+10=4
-4a=10
a= -5/2

P(3)=2(3)^3+[5(3)^2]/2+10
P(3)=54+45/2+10
P(3)=173/2
P(3)=86.5

Hope it helps.

Answer 8

4=2(-2)^3-a(-2)^2+10
4=-16-4a+10
10=-4a
a=-5/2

P(3)=2(3)^3-(-5/2)(3)^2+10
=2*27+(5*9/2)+10
=54+10+22.5=86.5

Answer 9

a=-2.5
P(3)=86.5