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Julli [10]
3 years ago
13

Help me please !!!!!

Mathematics
1 answer:
Natalka [10]3 years ago
8 0

Answer: DO you still need help I'll edit my answer if you do.

Step-by-step explanation:

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Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)
jeyben [28]

Answer:

The vertex: (\frac{3}{4},-\frac{41}{4} )

The vertical intercept is: y=-8

The coordinates of the two intercepts of the parabola are (\frac{3+\sqrt{41} }{4} , 0) and (\frac{3-\sqrt{41} }{4} , 0)

Step-by-step explanation:

To find the vertex of the parabola 4x^2-6x-8 you need to:

1. Find the coefficients <em>a</em>, <em>b</em>, and <em>c </em>of the parabola equation

<em>a=4, b=-6, \:and \:c=-8</em>

2. You can apply this formula to find x-coordinate of the vertex

x=-\frac{b}{2a}, so

x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex (f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c)

f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

\mathrm{Add\:}8\mathrm{\:to\:both\:sides}

x^2-6x-8+8=0+8

\mathrm{Simplify}

4x^2-6x=8

\mathrm{Divide\:both\:sides\:by\:}4

\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2

\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2

x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}

\left(x-\frac{3}{4}\right)^2=\frac{41}{16}

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}

4 0
3 years ago
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is 2.6 pie meters lo
pogonyaev
1.3 meters because the radius is half of the diameter, which is 2.6
5 0
3 years ago
PLEASE HELP!!
ElenaW [278]

Answer:

-1 and -3

(n+7)(n-8)

Step-by-step explanation:

1. Find the Zeros

f(x)=x^{2} +4x+3

f(x)=\left(x+1\right)\left(x+3\right)

x+1=0\\x=-1\\x+3=0\\x=-3

2. Factoring Trinomials

f(x)=n^{2} -n-56

f(x)=\left(n+7\right)\left(n-8\right)

n+7=0\\n=-7\\n-8=0\\n=8

4 0
3 years ago
Problem Page
LenKa [72]
2:7 , 2 to 7, 2/7 <====
4 0
3 years ago
Evaluate 7m+ 3mn when m=8 and n=14?Answers:aA:84,B:196,C:392,D=168​
Aleksandr-060686 [28]

Answer:

c) 392

Step-by-step explanation:

4 0
3 years ago
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