Graph F(x)=3x^2-3 - Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Graph f(x)=3x^2-3 Step 1Find the properties of the given parabola.Tap for more steps...Step 1.1Rewrite the equation in vertex form.Tap for more steps...Step 1.1.1Complete the square for .Tap for more steps...Step 1.1.1.1Use the form , to find the values of , , and .Step 1.1.1.2Consider the vertex form of a parabola.Step 1.1.1.3Find the value of using the formula .Tap for more steps...Step 1.1.1.3.1Substitute the values of and into the formula .Step 1.1.1.3.2Simplify the right side.Tap for more steps...Step 1.1.1.3.2.1Cancel the common factor of and .Tap for more steps...Step 1.1.1.3.2.1.1Factor out of .Step 1.1.1.3.2.1.2Cancel the common factors.Tap for more steps...Step 1.1.1.3.2.1.2.1Factor out of .Step 1.1.1.3.2.1.2.2Cancel the common factor.Step 1.1.1.3.2.1.2.3Rewrite the expression.Step 1.1.1.3.2.2Cancel the common factor of and .Tap for more steps...Step 1.1.1.3.2.2.1Factor out of .Step 1.1.1.3.2.2.2Cancel the common factors.Tap for more steps...Step 1.1.1.3.2.2.2.1Factor out of .Step 1.1.1.3.2.2.2.2Cancel the common factor.Step 1.1.1.3.2.2.2.3Rewrite the expression.Step 1.1.1.3.2.2.2.4Divide by .Step 1.1.1.4Find the value of using the formula .Tap for more steps...Step 1.1.1.4.1Substitute the values of , and into the formula .Step 1.1.1.4.2Simplify the right side.Tap for more steps...Step 1.1.1.4.2.1Simplify each term.Tap for more steps...Step 1.1.1.4.2.1.1Raising to any positive power yields .Step 1.1.1.4.2.1.2Multiply by .Step 1.1.1.4.2.1.3Divide by .Step 1.1.1.4.2.1.4Multiply by .Step 1.1.1.4.2.2Add and .Step 1.1.1.5Substitute the values of , , and into the vertex form .Step 1.1.2Set equal to the new right side.Step 1.2Use the vertex form, , to determine the values of , , and .Step 1.3Since the value of is positive, the parabola opens up.Opens UpStep 1.4Find the vertex .Step 1.5Find , the distance from the vertex to the focus.Tap for more steps...Step 1.5.1Find the distance from the vertex to a focus of the parabola by using the following formula.Step 1.5.2Substitute the value of into the formula.Step 1.5.3Multiply by .Step 1.6Find the focus.Tap for more steps...Step 1.6.1The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.Step 1.6.2Substitute the known values of , , and into the formula and simplify.Step 1.7Find the axis of symmetry by finding the line that passes through the vertex and the focus.Step 1.8Find the directrix.Tap for more steps...Step 1.8.1The 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.Step 1.8.2Substitute the known values of and into the formula and simplify.Step 1.9Use the properties of the parabola to analyze and graph the parabola.Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Step 2Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.Tap for more steps...Step 2.1Replace the variable with in the expression.Step 2.2Simplify the result.Tap for more steps...Step 2.2.1Simplify each term.Tap for more steps...Step 2.2.1.1Raise to the power of .Step 2.2.1.2Multiply by .Step 2.2.2Subtract from .Step 2.2.3The final answer is .Step 2.3The value at is .Step 2.4Replace the variable with in the expression.Step 2.5Simplify the result.Tap for more steps...Step 2.5.1Simplify each term.Tap for more steps...Step 2.5.1.1Raise to the power of .Step 2.5.1.2Multiply by .Step 2.5.2Subtract from .Step 2.5.3The final answer is .Step 2.6The value at is .Step 2.7Replace the variable with in the expression.Step 2.8Simplify the result.Tap for more steps...Step 2.8.1Simplify each term.Tap for more steps...Step 2.8.1.1One to any power is one.Step 2.8.1.2Multiply by .Step 2.8.2Subtract from .Step 2.8.3The final answer is .Step 2.9The value at is .Step 2.10Replace the variable with in the expression.Step 2.11Simplify the result.Tap for more steps...Step 2.11.1Simplify each term.Tap for more steps...Step 2.11.1.1Raise to the power of .Step 2.11.1.2Multiply by .Step 2.11.2Subtract from .Step 2.11.3The final answer is .Step 2.12The value at is .Step 2.13Graph the parabola using its properties and the selected points.Step 3Graph the parabola using its properties and the selected points.Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Step 4

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