F(x)=(1+x2

Answered question

2022-04-02

F(x)=(1+x2

Answer & Explanation

user_27qwe

user_27qwe

Skilled2022-04-21Added 375 answers

f(x)=(1+x2)

Find the properties of the given parabola.

Rewrite the equation in vertex form.

y=(x+0)2+1

Use the vertex form, y=a(x-h)2+k, to determine the values of ah, and k.

a=1

h=0

k=1

Since the value of aa is positive, the parabola opens up.

Find the vertex (h,k).

(0,1)

Find p, the distance from the vertex to the focus.

14

Find the focus.

(0,54)

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

x=0

Find the directrix.

y=34

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

Direction: Opens Up

Vertex: (0,1)

Focus: (0,54)

Axis of Symmetry: x=0

Directrix: y=34

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-25-12011225

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex: (0,1)

Focus: (0,54)

Axis of Symmetry: x=0

Directrix: y=34

xy-25-12011225


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