Mathematics, 26.06.2019 02:00 mkhayaro

What are the vertex and x-intercepts of the graph of y=x2-2x-24 select one answer for the vertex and one for the x-intercepts

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Answer from: ninaaforever

Vertex (1,-25), Intercepts at (6,0) and (-4,0)

Step-by-step explanation:

Axis of symmetry = -b/2a = -(-2)/2(1) = 2/2 = 1 so x=1 is the equation of line

Plug x=1 into equation y=1-2-24=-25

factor for x-intercepts: (x-6)(x+4)

set them equal to zero: x-6=0 so x=6 x+4=0 so x= - 4

Answer from: pennygillbert

The vertex of the provided equation (1,-25)

The x intercepts are (-4,0) and (6,0).

Step-by-step explanation:

Consider the provided equation.

y=x^2-2x-24

Substitute y=0 to find x intercepts.

x^2-2x-24=0

The above equation can be written as:

x^2+4x-6x-24=0

x(x+4)-6(x+4)=0

(x+4)(x-6)=0

By zero product rule:If ab=0 then either a=0 or b=0

x+4=0 or x-6=0

x=-4 or x=6

Hence, the x intercepts are (-4,0) and (6,0).

If the equation is in the standard form y=a^2+bx+c then the expression $\frac{-b}{2a}$ gives the x coordinate of the vertex.

By comparing the provided equation with standard form we can concluded that: a=1, b=-2 and c=-24

Substitute the respective values in the expression $\frac{-b}{2a}$ we get x coordinates of the vertex:

$\frac{-(-2)}{2(1)}=\frac{2}{2}=1$

Hence, the value of x=1.

Now substitute the value of x in the provided equation to find the value of y.

y=(1)^2-2(1)-24

y=1-2-24

y=-25

Hence, the vertex of the provided equation (1,-25)

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

25 inches - 0.694 yards

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