Question

how would i do this, graphs

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Answer 1

@kirbykirby

Answer 2

@amoodarya

Answer 3

@kropot72

Answer 4

@nincompoop

Answer 5

Recall that you can write the equation of the parabola in the form \( a(x-h)^2+k\), where \(h\) represents the horizontal shifts and \(k\) represents the vertical shifts. The \(a\) is just the dilation factor, and your initial parabola is \(x^2\), so \(a=1\), and your parabola didn't undergo a dilation.. it just moved

In fact, the point \((h, k)\) will the the coordinates of your vertex. So, can you determine \(h\) and \(k \)?

Answer 6

4 and 2

Answer 7

not quite exactly. You are in the quadrant where the x-values are negatives, and the y-values are negative as well

Answer 8

-4 and -2

Answer 9

yes, so now you can plug it in the formula \(a(x-h)^2+k\)

Answer 10

what is k

Answer 11

oh never mind

Answer 12

1(x-(-(-4))^2+(-2)

Answer 13

would it be 14

Answer 14

looks almost right but there is an extra minus (x - (-4))^2 + (-2)

Answer 15

oh it won't evaluate to a number.. this is the equation for the parabola. The x remains a variable with no fixed value

Answer 16

\[x-(-4)^2+(-2)\]

Answer 17

Be careful for the parenthesis, it is very important to keep it where it is
\((x-(-4))^2 + (-2) \) is not the same as \(x-(-4)^2+(-2)\)

It's probably best though to start simplifying all the negatives signs though to write
\((x+4)^2-2\)

Answer 18

If you have an equation

y = f(x),

- when you replace x with x - h, the graph shifts h units horizontally (to the right if h is positive, and to the left if h is negative.
- when you replace y with y - k, the graph shifts k units vertically (up if k is positive, and down if k is negative.

Answer 19

The blue graph is

\(f(x) = x^2\)

The red graph has shifted 4 units left and 2 units down.

That means that x was replaced with x - (-4) = x + 4.
Also, y is replaced with y - (-2) = y + 2

Rewriting f(x) as y, we get

y = x^2

Applying the shifts, we get:

\(y + 2 = (x + 4)^2\)

Solving for y, we get:

\(y = (x + 4)^2 - 2\)

Now we replace y with f(x) to get:

\(f(x) = (x + 4)^2 - 2\)