In order to find the equation of a line in slope-intercept form , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

.

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get

Plugging in those values for and in the equation, and you get

In order to find the equation of a line in slope-intercept form , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

.

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get

Plugging in those values for and in the equation, and you get

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

Because we are given the vertex of the parabola, the easiest way to solve this problem will involve the use of the formula of a parabola in vertex form. The vertex form of a parabola is given by the following equation:

f(x) = a(x – h)2 + k, where (h, k) is the location of the vertex, and a is a constant.

Since the parabola has its vertex as (–3, 4), its equation in vertex form must be as follows:

f(x) = a(x – (–3)2 + 4 = a(x + 3)2 + 4

In order to complete the equation for the parabola, we must find the value of a. We can use the point (–1, –4), through which the parabola passes, in order to determine the value of a. We can substitute –1 in for x and –4 in for f(x).

f(x) = a(x + 3)2 + 4

–4 = a(–1 + 3)2 + 4

–4 = a(2)2 + 4

–4 = 4_a_ + 4

Subtract 4 from both sides.

–8 = 4_a_

Divide both sides by 4.

a = –2

This means that the final vertex form of the parabola is equal to f(x) = –2(x + 3)2 + 4. However, since the answer choices are given in standard form, not vertex form, we must expand our equation for f(x) and write it in standard form.

f(x) = –2(x + 3)2 + 4

= –2(x + 3)(x + 3) + 4

We can use the FOIL method to evaluate (x + 3)(x + 3).

= –2(x_2 + 3_x + 3_x_ + 9) + 4

= –2(x_2 + 6_x + 9) + 4

= –2_x_2 – 12_x_ – 18 + 4

= –2_x_2 – 12_x_ – 14

The answer is f(x) = –2_x_2 – 12_x_ – 14.

Because we are given the vertex of the parabola, the easiest way to solve this problem will involve the use of the formula of a parabola in vertex form. The vertex form of a parabola is given by the following equation:

f(x) = a(x – h)2 + k, where (h, k) is the location of the vertex, and a is a constant.

Since the parabola has its vertex as (–3, 4), its equation in vertex form must be as follows:

f(x) = a(x – (–3)2 + 4 = a(x + 3)2 + 4

In order to complete the equation for the parabola, we must find the value of a. We can use the point (–1, –4), through which the parabola passes, in order to determine the value of a. We can substitute –1 in for x and –4 in for f(x).

f(x) = a(x + 3)2 + 4

–4 = a(–1 + 3)2 + 4

–4 = a(2)2 + 4

–4 = 4_a_ + 4

Subtract 4 from both sides.

–8 = 4_a_

Divide both sides by 4.

a = –2

This means that the final vertex form of the parabola is equal to f(x) = –2(x + 3)2 + 4. However, since the answer choices are given in standard form, not vertex form, we must expand our equation for f(x) and write it in standard form.

f(x) = –2(x + 3)2 + 4

= –2(x + 3)(x + 3) + 4

We can use the FOIL method to evaluate (x + 3)(x + 3).

= –2(x_2 + 3_x + 3_x_ + 9) + 4

= –2(x_2 + 6_x + 9) + 4

= –2_x_2 – 12_x_ – 18 + 4

= –2_x_2 – 12_x_ – 14

The answer is f(x) = –2_x_2 – 12_x_ – 14.

The point shifted to the right 5 units will shift along the x-axis, meaning that you will add 5 to the original x-coordinate, so the new . The point shifted down by three units will shift down the y-axis, meaning that you will subtract three from the original y-coordinate, so the new .

The resultant coordinate is .

The point shifted to the right 5 units will shift along the x-axis, meaning that you will add 5 to the original x-coordinate, so the new . The point shifted down by three units will shift down the y-axis, meaning that you will subtract three from the original y-coordinate, so the new .

The resultant coordinate is .