Question

Consider the following quadratic function.
f(x) = x2 − 6x − 7

Find the x- and y-intercepts of the graph, if any exist. (If an answer does not exist, enter DNE.)
x-intercept (x, y) = (larger x value)
x-intercept (x,y)= (smaller x value)

Convert the function into standard form.
f(x) =

Graph the quadratic function.


Identify the vertex and the axis of symmetry.
vertex
(x, y) =



axis of symmetry

Answer 1

Answer on Question #54913 - Math - Algebra

Consider the following quadratic function.

$$f (x) = x ^ {2} - 6 x - 7$$

Find the x- and y-intercepts of the graph, if any exist. (If an answer does not exist, enter DNE.)

x-intercept $(x,y) =$ (larger x value)

x-intercept $(x,y) =$ (smaller x value)

Convert the function into standard form.

$$f (x) =$$

Graph the quadratic function.

Identify the vertex and the axis of symmetry.

vertex

$$(x, y) =$$

Solution

Find the $x$ - and $y$ -intercepts of the graph, if any exist. (If an answer does not exist, enter DNE.)

$$x ^ {2} - 6 x - 7 = 0 \rightarrow | D = 6 ^ {2} - 4 \cdot (- 7) = 8 ^ {2} | \rightarrow x _ {1} = \frac {6 - 8}{2} = - 1, x _ {2} = \frac {6 + 8}{2} = 7$$ $$f (0) = 0 ^ {2} - 6 \cdot 0 - 7 = - 7$$

Thus,

$$y - \text {intercept is} (x, y) = (0; - 7)$$ $$x - \text {intercept} (x, y) = (\text {larger} x \text { value}) = - 1$$ $$x - \text {intercept} (x, y) = (\text {smaller} x \text { value}) = 7$$

Convert the function into standard form.

$$f (x) = x ^ {2} - 6 x + 9 - 9 + 7 = (x - 3) ^ {2} - 2$$

Graph the quadratic function.

Identify the vertex and the axis of symmetry.

vertex is

$$(x, y) = (3; - 2)$$

axis of symmetry is

$$x = 3$$

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