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2 years ago

10

Which equation has the least steep graph?

2 answers:

marshall27 [118]2 years ago

6 0

Y = 1/4x + 6.....this has a slope of 1/4 (or 0.25).....| 0.25 | = 0.25
y = -3/4x - 9....this has a slope of -3/4 (or - 0.75)...|-0.75 | = 0.75
y = 2x + 1.......this has a slope of 2...| 2 | = 2
y = -7x - 2......this has a slope of -7...| -7 | = 7

to find the least steep, take the lowest number of the absolute value of the slopes.

so the least steep graph is gonna be A. y = 1/4x + 6

wariber [46]2 years ago

5 0

Answer:y=1/4x+9

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

2 years ago

Please simplify 6-(2-4x)

umka2103 [35]

I'm pretty sure the answer would be 4+4x

6 0

2 years ago

Read 2 more answers

Solve for x<br> x ^2 +3x−4=0

Alla [95]

Answer:

= 1

= − 4

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

What is the solution -10 = 2a - 4

Simora [160]

Add 4 to both sides

-10 + 4 = 2a

Simplify -10 + 4 to -6

-6 = 2a

Divide both sides by 2

-6/2 = a

Simplify 6/2 to 3

-3 = a

Switch sides

<u>a = -3</u>

6 0

3 years ago

Read 2 more answers

What is the surface area of the prism?

cestrela7 [59]

Step 1: Find the area of the bases (triangles)

A = 1/2 * base * height

A = 1/2 * 16 * 6

A = 48

48 + 48 = 96

Area of the triangles = 96 cm^2

Step 2: Find the area of the sides (rectangles)

A = base * height

A1 = 16 * 12

A1 = 192

A2 = 10 * 12

A2 = 120

120 + 120 = 240

240 + 192 = 432 cm^2

Step 2: Add the areas together

96 + 432

528 cm^2

Hope this helps!! :)

5 0

2 years ago