Graph y=x^2*6

y=x2⋅6
Move 6 to the left of x2.
y=6×2
Find the properties of the given parabola.
Rewrite the equation in vertex form.
Complete the square for 6×2.
Use the form ax2+bx+c, to find the values of a, b, and c.
a=6,b=0,c=0
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(6)
Simplify the right side.
Cancel the common factor of 0 and 2.
Factor 2 out of 0.
d=2(0)2(6)
Cancel the common factors.
Cancel the common factor.
d=2⋅02⋅6
Rewrite the expression.
d=06
d=06
d=06
Cancel the common factor of 0 and 6.
Factor 6 out of 0.
d=6(0)6
Cancel the common factors.
Factor 6 out of 6.
d=6⋅06⋅1
Cancel the common factor.
d=6⋅06⋅1
Rewrite the expression.
d=01
Divide 0 by 1.
d=0
d=0
d=0
d=0
Find the value of e using the formula e=c-b24a.
Simplify each term.
Raising 0 to any positive power yields 0.
e=0-04⋅6
Multiply 4 by 6.
e=0-024
Divide 0 by 24.
e=0-0
Multiply -1 by 0.
e=0+0
e=0+0
e=0
e=0
Substitute the values of a, d, and e into the vertex form a(x+d)2+e.
6×2
6×2
Set y equal to the new right side.
y=6×2
y=6×2
Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=6
h=0
k=0
Since the value of a is positive, the parabola opens up.
Opens Up
Find the vertex (h,k).
(0,0)
Find p, the distance from the vertex to the focus.
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⋅6
Multiply 4 by 6.
124
124
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.
(0,124)
(0,124)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=0
Find the directrix.
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=-124
y=-124
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex: (0,0)
Focus: (0,124)
Axis of Symmetry: x=0
Directrix: y=-124
Direction: Opens Up
Vertex: (0,0)
Focus: (0,124)
Axis of Symmetry: x=0
Directrix: y=-124
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.
Replace the variable x with -1 in the expression.
f(-1)=6(-1)2
Simplify the result.
Raise -1 to the power of 2.
f(-1)=6⋅1
Multiply 6 by 1.
f(-1)=6
6
6
The y value at x=-1 is 6.
y=6
Replace the variable x with -2 in the expression.
f(-2)=6(-2)2
Simplify the result.
Raise -2 to the power of 2.
f(-2)=6⋅4
Multiply 6 by 4.
f(-2)=24
24
24
The y value at x=-2 is 24.
y=24
Replace the variable x with 1 in the expression.
f(1)=6(1)2
Simplify the result.
One to any power is one.
f(1)=6⋅1
Multiply 6 by 1.
f(1)=6
6
6
The y value at x=1 is 6.
y=6
Replace the variable x with 2 in the expression.
f(2)=6(2)2
Simplify the result.
Raise 2 to the power of 2.
f(2)=6⋅4
Multiply 6 by 4.
f(2)=24
24
24
The y value at x=2 is 24.
y=24
Graph the parabola using its properties and the selected points.
xy-224-160016224
xy-224-160016224
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex: (0,0)
Focus: (0,124)
Axis of Symmetry: x=0
Directrix: y=-124
xy-224-160016224
Graph y=x^2*6