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3 years ago

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 a, b, and c of the parabola equation

$a=4, b=-6, \:and \:c=-8$

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 <====

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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