Solve f(x)=-2x^2+8x+4 | Microsoft Math Solver

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Factor

- 2 (x - (2 - 6)) (x - (6 + 2))

Steps Using the Quadratic Formula

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

Quadratic polynomial can be factored using the transformation

a x^{2} + b x + c = a (x - x_{1}) (x - x_{2})

, where

x_{1}

and

x_{2}

are the solutions of the quadratic equation

a x^{2} + b x + c = 0

.

- 2 x^{2} + 8 x + 4 = 0

All equations of the form

a x^{2} + b x + c = 0

can be solved using the quadratic formula:

\frac{- b \pm b ^{2} - 4 a c}{2 a}

. The quadratic formula gives two solutions, one when

\pm

is addition and one when it is subtraction.

x = \frac{- 8 \pm 8 ^{2} - 4 ( - 2 ) \times 4}{2 ( - 2 )}

Square

8

.

x = \frac{- 8 \pm 6 4 - 4 ( - 2 ) \times 4}{2 ( - 2 )}

Multiply

- 4

times

- 2

.

x = \frac{- 8 \pm 6 4 + 8 \times 4}{2 ( - 2 )}

Multiply

8

times

4

.

x = \frac{- 8 \pm 6 4 + 3 2}{2 ( - 2 )}

Add

64

to

32

.

x = \frac{- 8 \pm 9 6}{2 ( - 2 )}

Take the square root of

96

.

x = \frac{- 8 \pm 4 6}{2 ( - 2 )}

Multiply

2

times

- 2

.

x = \frac{- 8 \pm 4 6}{- 4}

Now solve the equation

x = \frac{- 8 \pm 4 6}{- 4}

when

\pm

is plus. Add

- 8

to

46 \approx 9.797958971

.

x = \frac{4 6 - 8}{- 4}

Divide

- 8 + 46 \approx 1.797958971

by

- 4

.

x = 2 - 6

Now solve the equation

x = \frac{- 8 \pm 4 6}{- 4}

when

\pm

is minus. Subtract

46 \approx 9.797958971

from

- 8

.

x = \frac{- 4 6 - 8}{- 4}

Divide

- 8 - 46 \approx - 17.797958971

by

- 4

.

x = 6 + 2

Factor the original expression using

a x^{2} + b x + c = a (x - x_{1}) (x - x_{2})

. Substitute

2 - 6 \approx - 0.449489743

for

x_{1}

and

2 + 6 \approx 4.449489743

for

x_{2}

.

- 2 x^{2} + 8 x + 4 = - 2 (x - (2 - 6)) (x - (6 + 2))

Evaluate

4 + 8 x - 2 x^{2}

Graph

Quiz

10 problems similar to:

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

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Similar Problems from Web Search

How do you put the equation

f (x) = - 2 x^{2} + 8 x + 1

into a form that can be graphed?

https://socratic.org/questions/how-do-you-put-the-equation-f-x-2x-2-8x-1-into-a-form-that-can-be-graphed

Michael May 27, 2015 graph{ -2x^2+8x+1 [-10.62, 9.38, -19.385, -9.385] }

How do I convert

f (x) = - 2 x^{2} + 2 x + 4

to standard form ?

https://socratic.org/questions/how-do-i-convert-f-x-2x-2-2x-4-to-standard-form

(y - \frac{9}{2}) = - 2 (x - \frac{1}{2})^{2}

Explanation: Given f(x)= y=

- 2 x^{2} + 2 x + 4

- 2 (x^{2} - x) + 4

What is the graph of

f (x) = - 2 x^{2} + 7 x + 4

https://socratic.org/questions/what-is-the-graph-of-f-x-2x-2-7x-4

check the explanation below. Explanation:

y = - 2 x^{2} + 7 x + 4

Take -2 as a common factor from the first two terms and complete the square afterwards

y = - 2 (x^{2} - \frac{7}{2} x) + 4

How do you find the intercepts, vertex and graph

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

https://socratic.org/questions/how-do-you-find-the-intercepts-vertex-and-graph-f-x-2x-2-8x-3

(2, 5)

(3.58, 0); (0.42, 0)

(0, - 3)

How do you find the domain and range of

f (x) = - 2 x^{2} + 8 x - 5

https://socratic.org/questions/how-do-you-find-the-domain-and-range-of-f-x-2x-2-8x-5

x \in R

f (x) \leq 3

Explanation: First we can conisder the domain, this is fairly simple, we must consider what values ...

f (x) = 2 x^{2} + 8 x + 13 ?

https://math.stackexchange.com/q/1832512

This function does not have an inverse as it is not injective: check that

f (x - 2) = f (- x - 2)

x

is - for example,

f (1) = f (- 5)

, etc. We want to solve

y = 2 x^{2} + 8 x + 13

x

. Applying the ...

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-2x^{2}+8x+4=0

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

x=\frac{-8±\sqrt{8^{2}-4\left(-2\right)\times 4}}{2\left(-2\right)}

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=\frac{-8±\sqrt{64-4\left(-2\right)\times 4}}{2\left(-2\right)}

Square 8.

x=\frac{-8±\sqrt{64+8\times 4}}{2\left(-2\right)}

Multiply -4 times -2.

x=\frac{-8±\sqrt{64+32}}{2\left(-2\right)}

Multiply 8 times 4.

x=\frac{-8±\sqrt{96}}{2\left(-2\right)}

Add 64 to 32.

x=\frac{-8±4\sqrt{6}}{2\left(-2\right)}

Take the square root of 96.

x=\frac{-8±4\sqrt{6}}{-4}

Multiply 2 times -2.

x=\frac{4\sqrt{6}-8}{-4}

Now solve the equation x=\frac{-8±4\sqrt{6}}{-4} when ± is plus. Add -8 to 4\sqrt{6}\approx 9.797958971.

x=2-\sqrt{6}

Divide -8+4\sqrt{6}\approx 1.797958971 by -4.

x=\frac{-4\sqrt{6}-8}{-4}

Now solve the equation x=\frac{-8±4\sqrt{6}}{-4} when ± is minus. Subtract 4\sqrt{6}\approx 9.797958971 from -8.

x=\sqrt{6}+2

Divide -8-4\sqrt{6}\approx -17.797958971 by -4.

-2x^{2}+8x+4=-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\right)\right)

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 2-\sqrt{6}\approx -0.449489743 for x_{1} and 2+\sqrt{6}\approx 4.449489743 for x_{2}.

Examples

Quadratic equation

x^{2} - 4 x - 5 = 0

4 sin θ cos θ = 2 sin θ

Linear equation

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Simultaneous equation

{8 x + 2 y = 46 7 x + 3 y = 47

Differentiation

\frac{d}{d x} \frac{( 3 x ^{2} - 2 )}{( x - 5 )}

\int_{0}^{1} x e^{- x^{2}} d x

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}

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