For Question 2: Use the graph and equation provided to find the requested information You can earn: - 2 pts for each blank (1 pt will be given for an incomplete or poorly formatted response) 2. Given f(x)=(1)/(2) x^2+2 x-6 Identify the following information: y -intercept & x -intercept(s) & vertex & Axis of symmetry &

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Answer 1

To find the requested information for the quadratic function \( f(x) = \frac{1}{2}x^2 + 2x - 6 \), we will analyze the equation step by step.###

-intercept:The

-intercept occurs where

. Substitute

into the function:

So, the

-intercept is

.###

-intercept(s):The

-intercepts occur where \( f(x) = 0 \). Set the equation to zero and solve for

:

Multiply through by 2 to clear the fraction:

Now, factor the quadratic:

Setting each factor equal to zero gives:

Thus, the

-intercepts are

and

.### Vertex:The vertex of a parabola in the form

can be found using the formula for the

-coordinate of the vertex:

Here,

and

. So,

Substitute

back into the function to find the

-coordinate:

Therefore, the vertex is \((-2, -8)\).### Axis of symmetry:The axis of symmetry for a parabola given by

is the vertical line that passes through the vertex. It has the equation:

From our previous calculation, this is:

So, the axis of symmetry is

.In summary, the information is as follows:

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