Question

consider the quadratic function below and (a) find the vertex, (b) find the axis of symmetry, (c) determine whether there is a maximum or a minimum value, and find that value, and (d) graph the function.

(f(x) = x^2 - 12x + 35)

(a) the vertex occurs at ((6, -1)).
(type an ordered pair, using integers or fractions.)

(b) find an equation for the axis of symmetry.

6
(type an equation. use integers or fractions for any numbers in the equation.)

(c) determine whether the parabola has a maximum or a minimum and find its value.

select the correct choice below and fill in the answer box within your choice.
(type an integer or a fraction.)

a. the parabola opens downward and has a maximum value of
b. the parabola opens upward and has a minimum value of (-1)

(d) use the graphing tool on the right to graph the function.

Explanation:

Find the vertex of the parabola

Using the Quadratic Vertex Formula and Vertex of a Parabola knowledge points

$$
LATEXBLOCK0
$$

Find the axis of symmetry

The axis of symmetry is a vertical line passing through the \(x\)-coordinate of the vertex.

$$ x = 6 $$

Determine the extremum value

Since the leading coefficient \(a = 1 > 0\), the parabola opens upward.
Therefore, it has a minimum value at the vertex.
The minimum value is the \(y\)-coordinate of the vertex:

$$ \text{Minimum value} = -1 $$

Identify points for graphing

To graph the function, we find two points on either side of the vertex \( (6, -1) \).

$$
LATEXBLOCK1
$$

Answer:

Question 1

(a) The vertex occurs at <blank>\((6, -1)\)</blank>

Question 2

(b) Find an equation for the axis of symmetry: <blank>\(x = 6\)</blank>

Question 3

(c) Determine whether the parabola has a maximum or a minimum and find its value.

• A. The parabola opens downward and has a maximum value of ____
• B. The parabola opens upward and has a minimum value of \(-1\) (Correct answer)

Question 4

(d) Graph of the function \(f(x) = x^2 - 12x + 35\) with vertex at \((6, -1)\) and passing through \((5, 0)\) and \((7, 0)\).