Graph y=1/4*(x-2)^2+5

Find the properties of the given parabola.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens up.
Opens Up
Find the vertex .
Find , 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.
Substitute the value of into the formula.
Simplify.
Combine and .
Simplify by dividing numbers.
Divide by .
Divide by .
Find the focus.
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
Replace the variable with in the expression.
Simplify the result.
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify each term.
Raising to any positive power yields .
Multiply by .
Multiply by .
Multiply by .
Simplify the expression.
Divide by .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify each term.
One to any power is one.
Multiply by .
Multiply by .
Subtract from .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Divide by .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
The value at is .
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Graph y=1/4*(x-2)^2+5