Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

graph $g(x)=(x+5)^2-2$

View step-by-step help

View step-by-step help

Find derivatives using the chain rule I

Full solution

Q. graph

g(x)=(x+5)^2-2

Identify Function: Identify the function to be graphed. The function is $g(x)=(x+5)^2-2$ , which is a quadratic function in the form of $g(x)=a(x-h)^2+k$ , where $(h,k)$ is the vertex of the parabola.
Determine Vertex: Determine the vertex of the parabola. The vertex form of the quadratic function gives us the vertex directly. For $g(x)=(x+5)^2-2$ , the vertex is $(-5, -2)$ .
Analyze Direction: Analyze the direction of the parabola. Since the coefficient of the squared term $(x+5)^2$ is positive, the parabola opens upwards.
Find Axis of Symmetry: Find the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex. For the function $g(x)=(x+5)^2-2$ , the axis of symmetry is $x=-5$ .
Determine Y-Intercept: Determine the y-intercept. To find the y-intercept, set $x=0$ and solve for $g(x)$ . $g(0)=(0+5)^2-2=25-2=23$ . The y-intercept is $(0, 23)$ .
Plot Points: Plot the vertex, axis of symmetry, and $y$ -intercept on a coordinate plane. Use these points to sketch the parabola, making sure it opens upwards and is symmetric about the axis of symmetry.

More problems from Find derivatives using the chain rule I

Question

Find the derivative of

f(x)

\newline

f(x) = \cos(x)

\newline

f'(x) =

Posted 1 month ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan(x)

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^x

\newline

f'\left(x\right) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \ln(x)

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan^{-1}{x}

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \frac{e^x}{x}

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^{(x + 1)}

\newline

f'\left(x\right) =

Posted 1 month ago

Question

Find the derivative of

f(x)

\newline

f(x) = \sqrt{x+3}

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

g(x)

\newline

g(x) = \ln(2x)

\newline

g^{\prime}(x) =

Posted 3 months ago