Question

Y = x² – 4 y = 2r + 4​Solve algebraicallu for the solutions of equations below.

Answer 1

Step-by-step explanation:

Okay, the first step is to rewrite this equation in "vertex form." You can search that up but it's basically just (h/k).

y = ( x − 1) 2 + 3

Now, we are going to use the vertex form, "y = a (x - h)2 + k, to get the values of a, h, and k.

By using the form we get 1 for the value a, 1 for the value h, and 3 for the value k.

1 = a

1 = h

3 = k

Becuse the value of a is positive, the parabola opens up!  (A parabola is the U shaped line in a graph, so that opens up.)

Now, we find the vertex (h,k)

which is (1,3)

Now we find the p from the vertex to the focus.  (vertext the top, focus one of the points.)

Follow this formula to find the distance from the vertex to a focus by using this formula

1/4a.

Now we just gonna substitue 1 for a, since we know that 1 equals a above ^

1/4 * 1

Solving that, we got a nice little 1/4.

Next we find the focus

"Find the focus.

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

(h,k+p)

Substitute the known values of h, p, and k into the formula and simplify.

(1,134)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=1

Find the directrix.

y=114

Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.

xy−1704132437

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

xy−17041324"

(Sorry if this is long! But I hope you understand it better now! Thanks for the points!)