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Complete the square to re-write the quadratic function in vertex form:

y=x^(2)-x-1
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}-x-1$ $\newline$ Answer: $y=$

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Solve exponential equations by rewriting the base

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

y=x^{2}-x-1

\newline

Answer:

y=

Identify Coefficients: Identify the coefficients of $x^2$ and $x$ in the quadratic function. $\newline$ The coefficient of $x^2$ is $1$ , and the coefficient of $x$ is $-1$ . We will use these to complete the square.
Divide and Square: Divide the coefficient of $x$ by $2$ and square the result to find the value to add and subtract to complete the square. $\newline$ The coefficient of $x$ is $-1$ , so we divide it by $2$ to get $-\frac{1}{2}$ , and then square it to get $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ .
Add/Subtract to Complete: Add and subtract the value found in Step $2$ inside the function. $\newline$ We add and subtract $\frac{1}{4}$ inside the function to complete the square. $\newline$ $y = x^2 - x + \frac{1}{4} - \frac{1}{4} - 1$
Group and Combine: Group the terms to form a perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - x + \frac{1}{4}) - \frac{1}{4} - 1$ $\newline$ $y = (x - \frac{1}{2})^2 - \frac{1}{4} - 1$
Combine Constants: Combine the constants to simplify the equation. $\newline$ We combine $-\frac{1}{4}$ and $-1$ , which is the same as $-\frac{1}{4} - \frac{4}{4}$ , to get $-\frac{5}{4}$ . $\newline$ $y = (x - \frac{1}{2})^2 - \frac{5}{4}$

More problems from Solve exponential equations by rewriting the base

Question

x

\newline

5^x=1

\newline

\newline

Write your answer in simplest form.

Posted 5 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

Posted 4 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

Posted 5 months ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 8 months ago

Question

x

\newline

7 = 9^x

\newline

Round your answer to the nearest thousandth.

Posted 4 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 7 months ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 4 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6x

\newline

f(x) = 6^x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 4 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant