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3 years ago

F(x) = -x^2 - 10x - 13, find f(-2)

Mathematics

1 answer:

SVEN [57.7K]3 years ago

8 0

Answer: f(-2) = 11

Concept:

Here, we need to understand the idea of evaluation.

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

f (-2) or x = -2

Given function

f(x) = -x² - 10x - 13

Substitute values into the function

f(-2) = -(-2)² - 10 (-2) - 13

Simplify exponents

f(-2) = -(4) - 10 (-2) - 13

Simplify by multiplication

f(-2) = 4 + 20 - 13

Simplify by addition/subtraction

f(-2) = 24 - 13

f(-2) = $\boxed{11}$

Hope this helps!! :)

Please let me know if you have any questions

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Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

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Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

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

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

The vertex is the point (8,4)

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Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

$(x-2)^{2}=2.5$

square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

$x=2(+)1.58=3.58$

$x=2(-)1.58=0.42$

Part 5) we have

$f(x)=-x^{2}+50x-264$

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

$-x^{2}+50x-264=0$

$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

Complete the squares

$-(x^{2}-50x+625)=264-625$

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$(x^{2}-50x+625)=361$

Rewrite as perfect squares

$(x-25)^{2}=361$

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$(x-25)=(+/-)19$

$x=25(+/-)19$

$x=25(+)19=44$

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$f(x)=-x^{2}+8x-10$

Convert to vertex form

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Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

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$f(x)-6=-(x^{2}-8x+16)$

Rewrite as perfect square

$f(x)-6=-(x-4)^{2}$

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

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Convert to vertex form

Group terms

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Rewrite as perfect squares

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Convert to vertex form

Factor 2 the leading coefficient

$2(x^{2}-2x)-2=0$

Complete the square

$2(x^{2}-2x+1)-2-2=0$

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Rewrite as perfect squares

$2(x-1)^{2}-4=0$

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This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

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Complete the square

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Rewrite as perfect squares

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