Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the zeros of the following quadratic function using the square root method. What are the
x-intercepts of the graph of the function?

F(x)=(2x+9)^(2)-32

Find the zeros of the following quadratic function using the square root method. What are the $x$ -intercepts of the graph of the function? $\newline$ $F(x)=(2 x+9)^{2}-32$

View step-by-step help

View step-by-step help

Quadratic equation with complex roots

Full solution

Q. Find the zeros of the following quadratic function using the square root method. What are the

x

-intercepts of the graph of the function?

\newline

F(x)=(2 x+9)^{2}-32

Set Function Equal to Zero: Set the function equal to zero to find the x-intercepts. $\newline$ $F(x) = (2x + 9)^2 - 32 = 0$
Isolate Squared Term: Isolate the squared term to use the square root method. $\newline$ $(2x + 9)^2 = 32$
Take Square Root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(2x + 9)^2} = \pm\sqrt{32}$ $\newline$ $2x + 9 = \pm\sqrt{32}$
Simplify Square Root: Simplify the square root of $32$ . $\newline$ $\sqrt{32} = \sqrt{(16 \times 2)} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$ $\newline$ $2x + 9 = \pm 4\sqrt{2}$
Subtract and Isolate: Subtract $9$ from both sides to isolate the term with $x$ . $\newline$ $2x = -9 \pm 4\sqrt{2}$
Divide to Solve: Divide both sides by $2$ to solve for $x$ . $x = \frac{-9 \pm 4\sqrt{2}}{2}$
Write Solutions: Write the solutions as two separate x-intercepts. $\newline$ $x = \frac{-9 + 4\sqrt{2}}{2}$ and $x = \frac{-9 - 4\sqrt{2}}{2}$

More problems from Quadratic equation with complex roots

Question

\newline

8i + 6i

\newline

\newline

Write your answer in the form

a + bi

Posted 5 months ago

Question

Find the complex conjugate of the given number.

\newline

4 + 10i

\newline

\newline

Write your answer in the form

a + bi

Posted 5 months ago

Question

\newline

\frac{{-4i}}{{-9i}}

\newline

\newline

Write your simplified answer in the form

a + bi

Posted 5 months ago

Question

Combine the like terms to create an equivalent expression.

\newline

7k-k+19=\boxed{\phantom{0}}

Posted 10 months ago

Question

Apply the distributive property to factor out the greatest common factor.

\newline

9+12 n=

Posted 5 months ago

Question

Solve the equation.

\newline

\begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}

Posted 10 months ago

Question

What is the amplitude of

y=-\sin (8 x-3)+5

\newline

Posted 8 months ago

Question

What is the period of

\newline

y=4 \sin (-2 x+7)-1 \text { ? }

\newline

Give an exact value.

\newline

Posted 8 months ago

Question

3 \cdot(3+20 i)=

\newline

Your answer should be a complex number in the form

a+b i

a

b

are real numbers.

Posted 10 months ago

Question

(35-23 i)+(13+25 i)=

\newline

Express your answer in the form

(a+b i)

Posted 8 months ago

Related topics

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