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3 years ago

What is the vertex of the function?

Mathematics

1 answer:

Romashka [77]3 years ago

8 0

Answer:

(4, -25)

Step-by-step explanation:

One way to answer this is to put the equation into vertex form.

f(x)= x^2 -8x -9 . . . . . given

Add and subtract the square of half the x-coefficient:

f(x) = x^2 -8x +(-8/2)^2 -9 -(-8/2)^2

f(x) = x^2 -8x +16 -25

f(x) = (x -4)^2 -25

Comparing this to the vertex form of a quadratic:

f(x) = a(x -h)^2 +k

we find that (h, k) = (4, -25). This is the vertex.

_____

Alternate solution

The line of symmetry for ...

f(x) = ax^2 +bx +c

is given by x = -b/(2a). For your given quadratic that line is ...

x = -(-8)/(2(1)) = 4

Evaluating f(4) gives the y-coordinate:

f(4) = 4^2 -8·4 -9 = -25

The vertex is (x, y) = (4, -25).

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4

Dmitry [639]

Answer:

$\boxed{\sf Standard-form :x + 4y -17=0 }\\$

$\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

$\longrightarrow x + 4y = 7\\$

Firstly convert it into slope intercept form of the line which is y = mx + x , as ;

$\longrightarrow 4y = -x + 7 \\$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\$

On comparing it to y = mx + c , we have ,

$\longrightarrow m =\dfrac{-1}{4}\\$

$\longrightarrow c =\dfrac{7}{4}\\$

Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}\\$

Now we may use point slope form of the line as ,

$\longrightarrow y - y_1 = m(x-x_1) \\$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\$

$\longrightarrow 4(y -5 ) =-1(x +3) \\$

$\longrightarrow 4y -20 = - x -3 \\$

$\longrightarrow x + 4y -20+3=0\\$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\$

6 0

2 years ago

Which set of ordered pairs belongs to a linear function?

masya89 [10]

Answer:

Hi there the correct answer will be is B) (-1,5), (1, 3), (3, 1), (5,0)

hope it helps to your question!

7 0

3 years ago

tanji creates a "square, circle" repeating pattern. Kenji creates a "Square, circle, trianglr, cricle" repeating pattern. if bot

RoseWind [281]

Both tanji & kenji have same number of circles i.e. 50 .

Step-by-step explanation:

Here we have , tanji creates a "square, circle" repeating pattern. Kenji creates a "Square, circle, triangle, circle" repeating pattern. if both tanji and kenji have 100 shapes in their patterns, . We need to find that which pattern contains more circles .Let's find out :

tanji creates a "square, circle"

it's given that tanji has 100 shapes and he is repeating this pattern . In this pattern circle comes 1 every time out of 2 shapes :

Total number of times circle = $\frac{100}{2}(1)$

Total number of times circle = $50$

Kenji creates a "Square, circle, triangle, circle"

it's given that tanji has 100 shapes and he is repeating this pattern . In this pattern circle comes 2 every time out of 4 shapes :

Total number of times circle = $\frac{100}{4}(2)$

Total number of times circle = $50$

Both tanji & kenji have same number of circles i.e. 50 .

3 0

3 years ago

1/4=something 8 plz help me

gayaneshka [121]

Answer:

1/4 = 0.25

Step-by-step explanation:

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Ahat [919]

16.17

(

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Explanation:

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, Angles are

∠

;

∠

and

∠

180

−

(

)

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sin

⋅

sin

16.17

(

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Step-by-step explanation:

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