Part 1: Identify key features and graph a parabola from standard form. Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2

a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)

b) What is the vertex of the parabola? (1 point)

c) What is the focus of the parabola? (2 points)

d) What is the directrix of the parabola? (2 points)

e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is

Therefore, the focus of the parabola is = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

the infinity sign

step-by-step explanation:

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.