Graph y=1/3x^2+4

Math
y=13×2+4
Find the properties of the given parabola.
Tap for more steps…
Rewrite the equation in vertex form.
Tap for more steps…
Combine 13 and x2.
y=x23+4
Complete the square for x23+4.
Tap for more steps…
Use the form ax2+bx+c, to find the values of a, b, and c.
a=13,b=0,c=4
Consider the vertex form of a parabola.
a(x+d)2+e
Substitute the values of a and b into the formula d=b2a.
d=02(13)
Simplify the right side.
Tap for more steps…
Cancel the common factor of 0 and 2.
Tap for more steps…
Factor 2 out of 0.
d=2(0)2(13)
Cancel the common factors.
Tap for more steps…
Cancel the common factor.
d=2⋅02(13)
Rewrite the expression.
d=013
d=013
d=013
Multiply the numerator by the reciprocal of the denominator.
d=0⋅3
Multiply 0 by 3.
d=0
d=0
Find the value of e using the formula e=c-b24a.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raising 0 to any positive power yields 0.
e=4-04(13)
Combine 4 and 13.
e=4-043
Multiply the numerator by the reciprocal of the denominator.
e=4-(0(34))
Multiply 0 by 34.
e=4-0
Multiply -1 by 0.
e=4+0
e=4+0
Add 4 and 0.
e=4
e=4
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
13⋅(x+0)2+4
13⋅(x+0)2+4
Set y equal to the new right side.
y=13⋅(x+0)2+4
y=13⋅(x+0)2+4
Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=13
h=0
k=4
Since the value of a is positive, the parabola opens up.
Opens Up
Find the vertex (h,k).
(0,4)
Find p, the distance from the vertex to the focus.
Tap for more steps…
Find the distance from the vertex to a focus of the parabola by using the following formula.
14a
Substitute the value of a into the formula.
14⋅13
Simplify.
Tap for more steps…
Combine 4 and 13.
143
Multiply the numerator by the reciprocal of the denominator.
1(34)
Multiply 34 by 1.
34
34
34
Find the focus.
Tap for more steps…
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.
(0,194)
(0,194)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=0
Find the directrix.
Tap for more steps…
The directrix of a parabola is the horizontal line found by subtracting p from the y-coordinate k of the vertex if the parabola opens up or down.
y=k-p
Substitute the known values of p and k into the formula and simplify.
y=134
y=134
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex: (0,4)
Focus: (0,194)
Axis of Symmetry: x=0
Directrix: y=134
Direction: Opens Up
Vertex: (0,4)
Focus: (0,194)
Axis of Symmetry: x=0
Directrix: y=134
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.
Tap for more steps…
Replace the variable x with -1 in the expression.
f(-1)=(-1)23+4
Simplify the result.
Tap for more steps…
Raise -1 to the power of 2.
f(-1)=13+4
To write 4 as a fraction with a common denominator, multiply by 33.
f(-1)=13+4⋅33
Combine 4 and 33.
f(-1)=13+4⋅33
Combine the numerators over the common denominator.
f(-1)=1+4⋅33
Simplify the numerator.
Tap for more steps…
Multiply 4 by 3.
f(-1)=1+123
Add 1 and 12.
f(-1)=133
f(-1)=133
The final answer is 133.
133
133
The y value at x=-1 is 133.
y=133
Replace the variable x with -2 in the expression.
f(-2)=(-2)23+4
Simplify the result.
Tap for more steps…
Raise -2 to the power of 2.
f(-2)=43+4
To write 4 as a fraction with a common denominator, multiply by 33.
f(-2)=43+4⋅33
Combine 4 and 33.
f(-2)=43+4⋅33
Combine the numerators over the common denominator.
f(-2)=4+4⋅33
Simplify the numerator.
Tap for more steps…
Multiply 4 by 3.
f(-2)=4+123
Add 4 and 12.
f(-2)=163
f(-2)=163
The final answer is 163.
163
163
The y value at x=-2 is 163.
y=163
Replace the variable x with 3 in the expression.
f(3)=(3)23+4
Simplify the result.
Tap for more steps…
Cancel the common factor of (3)2 and 3.
Tap for more steps…
Factor 3 out of (3)2.
f(3)=3⋅33+4
Cancel the common factors.
Tap for more steps…
Factor 3 out of 3.
f(3)=3⋅33(1)+4
Cancel the common factor.
f(3)=3⋅33⋅1+4
Rewrite the expression.
f(3)=31+4
Divide 3 by 1.
f(3)=3+4
f(3)=3+4
f(3)=3+4
Add 3 and 4.
f(3)=7
The final answer is 7.
7
7
The y value at x=3 is 7.
y=7
Replace the variable x with 1 in the expression.
f(1)=(1)23+4
Simplify the result.
Tap for more steps…
One to any power is one.
f(1)=13+4
To write 4 as a fraction with a common denominator, multiply by 33.
f(1)=13+4⋅33
Combine 4 and 33.
f(1)=13+4⋅33
Combine the numerators over the common denominator.
f(1)=1+4⋅33
Simplify the numerator.
Tap for more steps…
Multiply 4 by 3.
f(1)=1+123
Add 1 and 12.
f(1)=133
f(1)=133
The final answer is 133.
133
133
The y value at x=1 is 133.
y=133
Graph the parabola using its properties and the selected points.
xy-2163-113304113337
xy-2163-113304113337
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex: (0,4)
Focus: (0,194)
Axis of Symmetry: x=0
Directrix: y=134
xy-2163-113304113337
Graph y=1/3x^2+4

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top