Mathematics, 30.01.2020 09:45 fantasticratz2

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consider the quadratic function f(x)=x^2−5x−6.

determine the following: (enter all numerical answers as integers, fractions, or decimals):

the smallest x-intercept is x= .

the largest x-intercept is x= .

the y-intercept is y= .

the vertex is ( , ).

the line of symmetry has the equation

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Answer from: slawson4328

Part 1) The smallest x-intercept is x=-1

Part 2) The largest x-intercept is x=6

Part 3) The y-intercept is y=-6

Part 4) The vertex is the point (2.5,-12.25)

Part 5) The equation of the line of symmetry is x=2.5

Step-by-step explanation:

we have

$f(x)=x^{2}-5x-6$

step 1

Find the x-intercepts

we know that

The x-intercept is the value of x when the value of the function is equal to zero

equate the function to zero

$x^{2}-5x-6=0$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}-5x-6=0$

$a=1\\b=-5\\c=-6$

substitute in the formula

$x=\frac{-(-5)(+/-)\sqrt{-5^{2}-4(1)(-6)}} {2(1)}$

$x=\frac{5(+/-)\sqrt{49}} {2}$

$x=\frac{5(+/-)7} {2}$

$x=\frac{5(+)7} {2}=6$

$x=\frac{5(-)7} {2}=-1$

therefore

The x-intercepts are

x=-1 and x=6

The smallest x-intercept is x=-1

The largest x-intercept is x=6

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

For x=0

$f(0)=(0)^{2}-5(0)-6$

f(0)=-6

therefore

The y-intercept is y=-6

step 3

Find the vertex

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

(h,k) is the vertex

Convert the function into vertex form

$f(x)=x^{2}-5x-6$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+6=(x^{2}-5x)$

Complete the square, Remember to balance the equation by adding the same constants to each side

$f(x)+6+2.5^{2}=(x^{2}-5x+2.5^{2})$

$f(x)+12.25=(x^{2}-5x+6.25)$

Rewrite as perfect squares

$f(x)+12.25=(x-2.5)^{2}$

$f(x)=(x-2.5)^{2}-12.25$

The vertex is the point (2.5,-12.25)

step 4

Find the equation of the line of symmetry

we know that

In a vertical parabola the equation of the line of symmetry is equal to the x-coordinate of the vertex

we have

vertex (2.5,-12.25)

The x-coordinate of the vertex is 2.5

therefore

The equation of the line of symmetry is x=2.5

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

Answer from: Quest

The variables should add up to equal 1

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