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disa [49]
2 years ago
8

What are the roots of the function f(x) = x2 + 2x – 1? a. x = ± √ _ 2 b. x = − 1 ± √ _ 2 c. x = 2 ± √ _ 2 d. x = 1 ± √ _ 2

Mathematics
1 answer:
Masteriza [31]2 years ago
7 0

Step-by-step explanation:

Root of the function, where y = 0

f(x) = x² + 2x - 1

0 = x² + 2x - 1

x² + 2x - 1 = 0

x² + 2x = 1

x² + 2x + 1 = 1 + 1

(x + 1)² = 2

x + 1 = ±√2

x = -1 ± √2

Roots → x = -1 ± √2

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Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function int
vesna_86 [32]

Answer:

f(x) = 3(x -\frac{2}{3})^2 -\frac{22}{3}

The vertex is (\frac{2}{3}, -\frac{22}{3})

Step-by-step explanation:

For a general quadratic function the form is:

ax ^ 2 + bx + c

For the function

f(x) = 3x ^ 2 -4x -6

Take common factor 3.

f(x) = 3(x ^ 2 -\frac{4}{3}x - 2)

The values of the coefficients for the function within the parenthesis are the following: a = 1, b = -\frac{4}{3}, c = -2

Take the value of b and divide it by 2. Then, the result obtained squares it.

\frac{b}{2}= -\frac{2}{3}

(\frac{b}{2})^2=\frac{4}{9}

Add and subtract \frac{4}{9}

f(x) = 3([x ^ 2 -\frac{4}{3}x +\frac{4}{9}]- 2-\frac{4}{9})

Write the expression of the form

f(x) = (x-\frac{b}{2})^2 +k

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The vertex is (\frac{2}{3}, -\frac{22}{3})

3 0
3 years ago
1. Find p(-3) if p(x) = 4x3 - 5x2 + 7x - 10
SVETLANKA909090 [29]

Answer:

1) -184

2) 13(m^{4}) ^{2}-3(m^{4})+4

Step-by-step explanation:

For problem number 1, Let's start by substituting all the x's for -3

So the equation will look like

p(-3)=4(-3)^{3}-5(-3)^{2}+7(-3)-10

Now, lets simplify by solving the exponents

First we'll do -3^{3} which equals -27

Now we'll do -3^{2} which equals 9

So now our equation looks like

p(-3)=4(-27)-5(9)+7(-3)-10

Now, we are going to multiply all these numbers

First 4(-27) which equals -108

Now -5(9) which equals -45

And finally 7(-3) which equals -21

Now our equation looks like

p(-3)= -108-45-21-10

Now we can solve

-108-45-21-10=-184

8 0
4 years ago
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tatuchka [14]

Answer:

5.26%

Step-by-step explanation:

15/285=x/100. 15 is the amount of weight he wants to lose. x=5.26%

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3 years ago
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Y=x^2-25 is it linear?
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