select the approxiate value of x that is solutions for (x)=0 value f(x)=-3x^2+2x+8

## select the approxiate value of x that is solutions for (x)=0 value f(x)=-3x^2+2x+8

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# 2 Answers

Find the appropriate value(s) of x that is/are the solution(s) to f(x)=0 where f(x)=-3x^2+2x+8.

The values of x that make f(x) = 0 are called the Zeros of f(x). The Zeros are also the x-intercepts if they are real. If the Zeros are Imaginary then f(x) has no x-intercepts.

So we want to solve the Quadratic Equation 0=-3x^2+2x+8 for the x-values that make it true, its Zeros, a.k.a., Roots.

Let's use the Quadratic Formula to find the Zeros:

If 0 = ax^2 + bx + c, then

x = (- b ± sqrt(b^2-4ac))/(2a)

Identify parameters:

a = -3, the coefficient of x^2

b = 2, the coefficient of x

c = 8, the constant

Substitute:

x = (- 2 ± sqrt(2^2-4(-3)(8)))/(2(-3))

Simplify:

x = (- 2 ± sqrt(4+4(24)))/(-2(3))

The values of x that make f(x) = 0 are called the Zeros of f(x). The Zeros are also the x-intercepts if they are real. If the Zeros are Imaginary then f(x) has no x-intercepts.

So we want to solve the Quadratic Equation 0=-3x^2+2x+8 for the x-values that make it true, its Zeros, a.k.a., Roots.

Let's use the Quadratic Formula to find the Zeros:

If 0 = ax^2 + bx + c, then

x = (- b ± sqrt(b^2-4ac))/(2a)

Identify parameters:

a = -3, the coefficient of x^2

b = 2, the coefficient of x

c = 8, the constant

Substitute:

x = (- 2 ± sqrt(2^2-4(-3)(8)))/(2(-3))

Simplify:

x = (- 2 ± sqrt(4+4(24)))/(-2(3))

x = (- 2 ± sqrt(4(1+24)))/(-2(3))

x = (- 2 ± sqrt(4(25)))/(-2(3))

x = (- 2 ± 2*5)/(-2(3))

x = (1 ± 5)/3

x = -4/3 or 2

Hi again Michelle;

0=f(x)=-3x

^{2}+2x+8For the FOIL...

FIRST must be (3x)(x) and one number must be negative to produce -3x

^{2}.OUTER and INNER must add-up to 2x.

LAST must be (8)(1) or (1)(8) or (4)(2) or (2)(4) and both numbers must be positive to produce positive 8, as well as positive 2x for the OUTER and INNER.

0=(3x+4)(-x+2)

Let's FOIL...

FIRST...(3x)(-x)=-3x

^{2}OUTER...(3x)(2)=6x

INNER...(4)(-x)=-4x

LAST...(4)(2)=8

0=-3x

^{2}+6x-4x+80=-3x

^{2}+2x+8(3x+4)(-x+2)=0

Either or both parenthetical equations must equal zero.

3x+4=0

3x=-4

**x=-4/3**

-x+2=0

-x=-2

**x=2**