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Write the quadratic function in standard form.f(x) = x2 − 6x − 7f(x) = Give the vertex.(x, y) = Find the intercepts. (If an answer does not exist, enter DNE.)x-intercept (x, y) = (smaller x-value)x-intercept (x, y) = (larger x-value)y-intercept (x, y) =

User Ange Loron
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1 Answer

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Answers:

Standard form: f(x) = (x - 3)² - 16

vertex: (3, -16)

x-intercept (x, y) = (-1, 0)

x-intercept (x, y) = (7, 0)

y-intercept (x, y) = (0, -7)

Step-by-step explanation:

The given equation is

f(x) = x² - 6x - 7

To write in the standard form, we need to add and subtract (b/2)², where b is the number besides x, so replacing b = -6, we get:

(b/2)² = (-6/2)² = (-3)² = 9

Then, when we add and subtract 9, we get:

f(x) = x² - 6x + 9 - 9 - 7

f(x) = (x - 3)² - 16

Now, in an equation of the form y = (x - h)² + k, the vertex is (h, k). So, in this case, the vertex is (3, -16)

On the other hand, the y-intercept is the point where the line crosses the y-axis. It can be calculated replacing x by 0 on the equation of f(x), so

f(x) = x² - 6x - 7

f(0) = 0² - 6(0) - 7

f(0) = -7

Therefore, the y-intercept is the point (0, -7)

To find the x-intercepts, we need to make f(x) = 0, so

f(x) = x² - 6x - 7 = 0

(x - 7)(x + 1) = 0

Then

x - 7 = 0

x - 7 + 7 = 0 + 7

x = 7

and

x + 1 = 0

x + 1 - 1 = 0 - 1

x = -1

Therefore, the x-intercepts are (7, 0) and (-1, 0).

So, the answers are

Standard form: f(x) = (x - 3)² - 16

vertex: (3, -16)

x-intercept (x, y) = (-1, 0)

x-intercept (x, y) = (7, 0)

y-intercept (x, y) = (0, -7)

Then, the graph of the function is

Write the quadratic function in standard form.f(x) = x2 − 6x − 7f(x) = Give the vertex-example-1
User Jaap
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