Rewrite f(x) into vertex form by completing the square f(x)=−x2+8x+9

Mathematics

1 answer:

GalinKa [24]2 years ago

3 0

Answer:

vertex = ( 4 , 25 )

Step-by-step explanation:

given a parabola in standard form y = a x 2 + b x + c x ; a ≠ 0

then the x-coordinate of the vertex is

X vertex=-b/2a

y=-x2+8x+9 with a=-1 b=8 c=9

X vertex= -8/-2=4

substitute the value on the equation

Y vertex = -(4)squared+8(4)+9=25

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If f(x) = 3x22, evaluate afI: ()k=1

Korolek [52]

Step 1: Write out the function given

$f(x)=3x^2-x$

Step 2: Interprete the question given

$\sum ^5_{k\mathop=1}f(\frac{k}{2})$

The question requested we find the summation of the first five terms for f(k/2), when k is 1, 2, 3, 4, and 5

Step 3: Find the expression for f(k/2)

$\begin{gathered} f(\frac{k}{2})=3(\frac{k}{2})^2-\frac{k}{2} \\ =\frac{3k^2}{4}-\frac{k}{2} \\ =\frac{3k^2-2k}{4} \end{gathered}$ $\begin{gathered} =\frac{3(1)^2-2(1)}{4}+\frac{3(2)^2-2(2)}{4}+\frac{3(3)^2-2(3)}{4}+\frac{3(4)^2-2(4)}{4}+\frac{3(5)^2-2(5)}{4} \\ =\frac{1+8+21+40+65}{4} \\ =\frac{135}{4} \\ =33.75 \end{gathered}$

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5 0

11 months ago

In the xy-plane, the equations x + 2 = 10 y and 3 +6 = x y c represent the same line for some constant c. What is the value of c

aalyn [17]

Answer:

C=30

Step-by-step explanation:

Supposing that we have the lines

x+2=10y

and

3x+6=Yc.

Note that dividing by 3 the second line can be rewritten as

x + 2= Y c/3.

Remember that a line is written as $ax+b=dY$ , in our case, both lines have $a=1$ and $b=2$ . Therefore, in orther that the two lines are equal, we need that $10=c/3$ , hence $c=30.$