Help. Here's the question, could you please put the letter answer, please.

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

Please help with problems 6 and 7.

monitta

6 is A and seven is B

7 0

3 years ago

The table shows the results of spinning a four colored spinner 50 times. Find the experimental probability and express it as a d

gogolik [260]

Red is 20 and you spin it 50 times so 2/5 chance is red so that makes 3/5 chance not red

5 0

3 years ago

Answer this question please!

fomenos

$r_{2} = \frac{F_1 \sin(\theta)}{F_{2} \sin(\psi)}$

4 0

3 years ago

A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 49 cubic feet. What dime

yawa3891 [41]

Answer:

b = 4.6 ft

h = 2.3 ft

Step-by-step explanation:

The volume of the tank is given by:

$b^2*h=49$

Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.

The surface area can be written as:

$A=b^2+4bh\\A=b^2+4b*({\frac{49}{b^2}})\\A=b^2+\frac{196}{b}$

The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:

$\frac{dA}{db} =0=2b-\frac{196}{b^2}\\2b^3=196\\b=4.61\ ft$

The value of h is then:

$h=\frac{49}{4.61^2}\\h=2.31\ ft$

Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.

7 0

3 years ago