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3 years ago

What is the axis of symmetry of the function f(x) = –(x + 9)(x – 21)?

1 answer:

3 0

First, we have to realize that this is factored form, so we have to put this in standard quadratic form using FOIL, which is a rule mandating how we multiply the numbers here. F stands for First, which means the first number inside the parentheses for both of them, then O means the first number in the first quantity(fancy word for parentheses) multiplied by the last number of the second quantity, and so forth. When you are done, you combine like terms

anyway, you end up with x²-12x-189, but you have to inverse all numbers because of the parentheses in front, so it becomes -x²+12x+189.

Now you can find the axis of symmetry uisng the equation -b=2a (oh yeah, I forgot to mention: the standard quadratic form is a(x)²+b(x)+c already). So you do -12 / -2, which then becomes 6.

The axis of symmetry is 6

You might be interested in

Write the point-slope form of the given line that passes through the points (0, 3) and (4, 0). Identify (x1, y1) as the x-interc

Sindrei [870]

Now, bear in mind that, when the y-axis gets intercepted, x = 0, therefore 0,3 is really the y-intercept.

and when the x-axis gets intercepted, y = 0, therefore 4,0 is the x-intercept, thus we will use this one in the point-slope form then.

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 3}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 0}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-3}{4-0}\implies -\cfrac{3}{4}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-0=-\cfrac{3}{4}(x-4)$

5 0

3 years ago

I need some help please.

almond37 [142]

Answer:

Step-by-step explanation:

8 0

3 years ago

Solve (2/3)-(1/x)=5/6

Keith_Richards [23]

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$ Multiply both sides by 3
$2 - \frac{1(3)}{x} = \frac{5(3)}{6}$ Simplify the numerators
$2 - \frac{3}{x} = \frac{15}{6}$ Multiply both sides by 6
$12 - \frac{3(6)}{x} = 15$ Simplify the numerator
$12 - \frac{18}{x} = 15$ Multiply both sides by x
12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6

Check your answer by plugging -6 in for the x in the original problem:

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$ Plug in -6 for x
$\frac{2}{3} - \frac{1}{-6} = \frac{5}{6}$ Change $\frac{2}{3}$ to $\frac{4}{6}$ so all denominators are the same
$\frac{4}{6} - \frac{1}{-6} = \frac{5}{6}$ Change $\frac{1}{-6}$ to $\frac{-1}{6}$ for easier work
$\frac{4}{6} - \frac{-1}{6} = \frac{5}{6}$ Subtract the numerators (4 - (-1) )
$\frac{5}{6}$ = $\frac{5}{6}$

So, x = -6 .

5 0

3 years ago

Can anyone please help me with these

DochEvi [55]

Answer: Natural/Counting = 1, 0, 6, 3,

Whole = 1234, 135

Integers = -42,260, -97

Rational = 0.5432, 14.4, 6.2, 6.5892,

-14.4, 7.7777777, -13.574,

3.14, 0.4, 6.2, 0.4, 0.34,

12/6, -8/4, -10/5, -3/4, -3/8,

3/7, -4/8, 6/2, -8/4

Irrational = √34, -√34, -√ 36, 2π, √81,

√300, √1, π.

;Hope this Helped with both Pages:)

4 0

3 years ago

On a two question true or false quiz what is the probability of guessing both answer answer correctly

algol13

25% chance of guessing each question correctly

50% chance to guess one correctly

6 0

2 years ago