Please help. I don’t understand. Will give Brainly. Thank you!

Y=x^2-6x+3 help write the vertex form of the equation

Artist 52 [7]

Answer:

$y=(x-3)^2-6$

Step-by-step explanation:

$y=x^2-6x+3$

This is written in the standard form of a quadratic function:

$y=ax^2+bx+c$

where:

ax² → quadratic term
bx → linear term
c → constant

You need to convert this to vertex form:

$y=a(x-h)^2+k$

where:

(h,k) → vertex

To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

$x=-\frac{b}{2a}$

Using your original equation, identify the a, b, and c terms:

$a=1\\\\b=-6\\\\c=3$

Insert the known values into the equation:

$x=-\frac{(-6)}{2(1)}$

Simplify. Two negatives make a positive:

$x=\frac{6}{2} =3$

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

$y=3^2-6(3)+3$

Simplify using PEMDAS:

$y=9-18+3\\\\y=-9+3\\\\y=-6$

The value of y is -6 (3,-6). Insert these values into the vertex form:

$(3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)$

Insert the value of a and simplify:

$y=(x-3)^2-6$

:Done

6 0

3 years ago

10 dan büyük doğal sayılar 50 den küçük doğal sayılar 7 nın katı olan pozitif tam sayilar

shtirl [24]

Answer:

yes lul

Step-by-step explanation:

7 0

3 years ago

What is the effect on the graph of the function f(x) = 2^x when f(x) is replaced with f(x − 3)?

mel-nik [20]

Graph of f(x-3) is compressed by a factor of $\frac{1}{8}$ horizontally of f(x).

<u>Step-by-step explanation:</u>

We have, the graph of f(x)= $2^{x}$ , on replacing f(x) by f(x-3) we get:

$f(x-3)$ = $2^{x-3} = \frac{2^{x}}{2^{3}} = \frac{1}{8} 2^{x} = \frac{1}{8} f(x)$ .Below shown are the images for graph of f(x) and f(x-3). Both are functions are exponential , and so having exponential graph but f(x-3) is compressed by a factor of $\frac{1}{8}$ horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph : $f(x-3) = \frac{1}{8} f(x)$ .