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!)