Question

: What is the equation of the parabola in the vertex form.

0 = y^2 – x – 4y + 3

A: (x + 12)^2 = (y – 4)
B: (x+1) = (y-2)^2
C: (x-1) = (y+2)^2
D: (x-3) = (y-2)^2





: Graph the parabola. The graph scales 6 tall and 8 wide.

(x+2) = (y-3)^2

(x-2)^2 = 4(y+3)

(x+3)^2 = 4(y+2)

(x-2) = -4(y-3)^2


: What is the equation of the parabola, in vertex form, with vertex at (2, -4) and driectrix y = - 6

A: (y+6)^2 = -8(x+2)
B: (x+2)^2 = 8(y+4)
C: (x-2)^2 = 8(y+4)
D: (y+4)^2 = 8(x-2)


: If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?

X = - 8y^2

A: (x-3) = -8(y+2)^2

B: (x+2) = -8(y+3)^2

C: (x+3) = -8(y-2)^2

D: (x-2) = -8(y-3)^2

Answer 1

Answer on Question #57314 – Math – Analytic Geometry

Question

1. What is the equation of the parabola in the vertex form.

$$0 = y^2 - x - 4y + 3$$ $$A: (x + 12)^2 = (y - 4)$$ $$B: (x + 1) = (y - 2)^2$$ $$C: (x - 1) = (y + 2)^2$$ $$D: (x - 3) = (y - 2)^2$$

Solution:

$$y^2 - x - 4y + 3 = 0$$ $$(y^2 - 4y + 4) - 4 - x + 3 = 0$$ $$(y - 2)^2 = x + 1$$

Answer: B: $(x + 1) = (y - 2)^2$.

Question

2. Graph the parabola. The graph scales 6 tall and 8 wide.

a) $(x + 2) = (y - 3)^2$

b) $(x - 2)^2 = 4(y + 3)$

c) $(x + 3)^2 = 4(y + 2)$

d) $(x - 2) = -4(y - 3)^2$

Solution

a) $(x + 2) = (y - 3)^2$

This is a graph of horizontal parabola and it is shifted two units left and three units up.

b) $(x - 2)^{2} = 4(y + 3)$

This is a graph of vertical parabola and it is shifted two units right and three units down. The graph of the parabola is also compressed four times in the y-direction.

c) $(x + 3)^{2} = 4(y + 2)$ .

This is a graph of vertical parabola and it is shifted three units left and two units down. The graph of the parabola is also compressed four times in the y-direction.

d) $(x - 2) = -4(y - 3)^2$.

This is a graph of horizontal parabola and it is shifted two units right and three units up. The graph of the parabola is also compressed four times in the y-direction.

**Question**

3. What is the equation of the parabola, in vertex form, with vertex at (2, -4) and directrix $y = -6$?

A: $(y + 6)^2 = -8(x + 2)$

B: $(x + 2)^2 = 8(y + 4)$

C: $(x - 2)^2 = 8(y + 4)$

D: $(y + 4)^2 = 8(x - 2)$

Solution

If the equation of the parabola is $(x - h)^2 = 4p(y - k)$, then the vertex of this parabola is at $(h, k)$, the directrix is the line $y = k - p$.

It is given that $h = 2$, $k = -4$, $k - p = -6$, that is, $-4 - p = -6$, hence

$$p = 2.$$

Because the equation of the parabola is $(x - h)^2 = 4p(y - k)$, the answer is

$$\begin{array}{l} (x - 2)^2 = 4 \cdot 2(y + 4), \\ (x - 2)^2 = 8(y + 4), \end{array}$$

Answer: C: $(x - 2)^2 = 8(y + 4)$.

Question

4. If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation? $x = -8y^2$

A: $(x - 3) = -8(y + 2)^2$

B: $(x + 2) = -8(y + 3)^2$

C: $(x + 3) = -8(y - 2)^2$

D: $(x - 2) = -8(y - 3)^2$

Solution

First shift it two units left

$$x + 2 = -8y^2$$

Now we can shift it three units down

$$x + 2 = -8(y + 3)^2$$

Answer: B: $(x + 2) = -8(y + 3)^2$.

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