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Novay_Z [31]
3 years ago
7

find the x-intercepts and the coordinates of the vertex for the parabola Y equals negative X squared plus 8X -12. If there’s mor

e than one X intercept, separate them commas.
Mathematics
1 answer:
Oksanka [162]3 years ago
3 0

Answer:

x = 2, and 6

x = 2 , 6

Step-by-step explanation:

The quadratic function to analyze is: y = -x^2+8x-12

In order to find where the corresponding parabola intercepts the x axis, we set it equal to zero (y = 0):

y = -x^2+8x-12\\0 = -x^2+8x-12\\x^2-8x+12=0

This equation is easy to solve by factoring. We look for a air of integer numbers whose product equals the constant term "12", and whose combinig renders the coefficient of the middle term of the trinomial "-8".

The two such numbers are "-2" and "-6". We use them to split the middle term, and then solve by factoring by grouping:

x^2-8x+12=0\\x^2-2x-6x+12=0\\(x^2-2x)+(-6x+12)=0\\x(x-2)-6(x-2)=0\\(x-2)(x-6)=0

For the product of two factors to render zero, we need either one to be a zero.This means that (x-2)=0 (that is x = 2), or (x-6)=0 (that is x = 6).

So, there are two x-intercepts: x= 2, and 6

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What is the equation of the line that passes through the point (-1, -7) and has a<br> slope of 2?
slava [35]

Answer:

y=2x-5

Step-by-step explanation:

The slope-intercept form of an equation looks like y=mx+b. Where m is the slope and b is the y-intercept. The slope is already given to us, so m is 2.

To find b use the equation b=y_1-m*x_1. So, to find the y-intercept use b=-7-(2*-1). This equals b=-5.

So, plug in the values to get the final equation y=2x-5.

7 0
2 years ago
Read 2 more answers
Write the standard form equation of the ellipse shown in the graph, and identify the foci.
vlada-n [284]

Answer option A

From the given graph is a Vertical ellipse

Center of ellipse = (-2,-3)

Vertices are (-2,3)  and (-2,-9)

Co vertices are (-6,-3) and (2,-3)

The distance between center and vertices = 6, so a= 6

The distance between center and covertices = 4 , so b= 4

The general equation of vertical ellipse is

\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2}=1

(h,k) is the center

we know center is (-2,-3)

h= -2, k = -3 , a= 6  and b = 4

The standard equation  becomes

\frac{(x+2)^2}{4^2} + \frac{(y+3)^2}{6^2}=1

\frac{(x+2)^2}{16} + \frac{(y+3)^2}{36}=1

Foci  are (h,k+c)  and (h,k-c)

c=\sqrt{a^2-b^2}

Plug in the a=6  and b=4

c=\sqrt{6^2-4^2}

 c=\sqrt{20}

  c=2\sqrt{5}, we know h=-2  and k=-3

Foci  are   (-2,-3+2\sqrt{5})  and  (-2,-3-2\sqrt{5})

Option A is correct

6 0
3 years ago
Please answer i have more questions too​
aliina [53]
The rate of change is 16
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3 years ago
What is 32.043 in expanded form
natima [27]
<span>30 + 2 + 0.04 + 0.003</span>
7 0
3 years ago
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Does someone mind helping me with this question? Thank you!
BartSMP [9]

Answer:

41

Step-by-step explanation:

3(4)²-2(4)+1

48-8+1

41

6 0
1 year ago
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