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(PLEASE HELP ME WITH MY HOMEWORK!!)

1. Let g(x) = (x + 2)² - 4.
a. Identify the transformations that occurred from the parent function p(x) = x².
b. Identify the vertex of the parabola.
c. Graph y = g(x).

2. Three parabolas and their equations are given. Label each graph with its corect function name. f(x) = -x² g(x)=x²+1 k(x) = (x+3)²

3. Explain how you can tell if a parabola will open up or open down​

User Lostaunaum
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1 Answer

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1a)Horizontal shift left by 2 units (x + 2).

Vertical shift down by 4 units (- 4).

b) The vertex is (-2, -4)

c) g(x), the parabola opens upward with vertex (-2,-4).

2) Downward facing parabola.

Upward facing parabola, shifted up by 1 unit.

Upward facing parabola, shifted left by 3 units.

3) If ( a > 0 ), the parabola opens upward;

if ( a < 0 ), it opens downward.

What is a parabola?

Given

g(x) = (x + 2)² - 4, parent function p(x) = x²

a) Transformations from p(x) = x²:

Horizontal shift left by 2 units (x + 2).

Vertical shift down by 4 units (- 4).

b) Vertex of the Parabola:

y = a(x - h)² + k

Where

(h, k) is the vertex of the parabola.

a is a constant that determines the direction and width of the parabola.

If ( a > 0 ), the parabola opens upward;

if ( a < 0 ), it opens downward.

Compare with the general equation

h = -2, k = -4

The vertex is (-2, -4)

c)Graph of y = g(x), the parabola opens upward because a = 1 which is greater than 0.

2.Parabolas and Equations:

f(x) = -x²: Downward facing parabola.

g(x) = x² + 1: Upward facing parabola, shifted up by 1 unit.

k(x) = (x + 3)²: Upward facing parabola, shifted left by 3 units.

3.Parabola Direction (Opening Up or Down):

If the coefficient of the x² term is positive, the parabola opens upward.

If the coefficient of the x² term is negative, the parabola opens downward.

(PLEASE HELP ME WITH MY HOMEWORK!!) 1. Let g(x) = (x + 2)² - 4. a. Identify the transformations-example-1
(PLEASE HELP ME WITH MY HOMEWORK!!) 1. Let g(x) = (x + 2)² - 4. a. Identify the transformations-example-2
(PLEASE HELP ME WITH MY HOMEWORK!!) 1. Let g(x) = (x + 2)² - 4. a. Identify the transformations-example-3
(PLEASE HELP ME WITH MY HOMEWORK!!) 1. Let g(x) = (x + 2)² - 4. a. Identify the transformations-example-4
User NRewik
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