Graph F(x)=g(x)-3 - Mathway

Enter a problem... Trigonometry Examples Popular Problems Trigonometry Graph f(x)=g(x)-3 Step 1Find the standard form of the hyperbola.Tap for more steps...Step 1.1Move all terms containing variables to the left side of the equation.Tap for more steps...Step 1.1.1Subtract from both sides of the equation.Step 1.1.2Reorder and .Step 1.2Flip the sign on each term of the equation so the term on the right side is positive.Step 1.3Divide each term by to make the right side equal to one.Step 1.4Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .Step 2This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.Step 3Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .Step 4The center of a hyperbola follows the form of . Substitute in the values of and .Step 5Find , the distance from the center to a focus.Tap for more steps...Step 5.1Find the distance from the center to a focus of the hyperbola by using the following formula.Step 5.2Substitute the values of and in the formula.Step 5.3Simplify.Tap for more steps...Step 5.3.1Rewrite as .Tap for more steps...Step 5.3.1.1Use to rewrite as .Step 5.3.1.2Apply the power rule and multiply exponents, .Step 5.3.1.3Combine and .Step 5.3.1.4Cancel the common factor of .Tap for more steps...Step 5.3.1.4.1Cancel the common factor.Step 5.3.1.4.2Rewrite the expression.Step 5.3.1.5Evaluate the exponent.Step 5.3.2Rewrite as .Tap for more steps...Step 5.3.2.1Use to rewrite as .Step 5.3.2.2Apply the power rule and multiply exponents, .Step 5.3.2.3Combine and .Step 5.3.2.4Cancel the common factor of .Tap for more steps...Step 5.3.2.4.1Cancel the common factor.Step 5.3.2.4.2Rewrite the expression.Step 5.3.2.5Evaluate the exponent.Step 5.3.3Add and .Step 6Find the vertices.Tap for more steps...Step 6.1The first vertex of a hyperbola can be found by adding to .Step 6.2Substitute the known values of , , and into the formula and simplify.Step 6.3The second vertex of a hyperbola can be found by subtracting from .Step 6.4Substitute the known values of , , and into the formula and simplify.Step 6.5The vertices of a hyperbola follow the form of . Hyperbolas have two vertices.Step 7Find the foci.Tap for more steps...Step 7.1The first focus of a hyperbola can be found by adding to .Step 7.2Substitute the known values of , , and into the formula and simplify.Step 7.3The second focus of a hyperbola can be found by subtracting from .Step 7.4Substitute the known values of , , and into the formula and simplify.Step 7.5The foci of a hyperbola follow the form of . Hyperbolas have two foci.Step 8Find the eccentricity.Tap for more steps...Step 8.1Find the eccentricity by using the following formula.Step 8.2Substitute the values of and into the formula.Step 8.3Simplify.Tap for more steps...Step 8.3.1Simplify the numerator.Tap for more steps...Step 8.3.1.1Rewrite as .Tap for more steps...Step 8.3.1.1.1Use to rewrite as .Step 8.3.1.1.2Apply the power rule and multiply exponents, .Step 8.3.1.1.3Combine and .Step 8.3.1.1.4Cancel the common factor of .Tap for more steps...Step 8.3.1.1.4.1Cancel the common factor.Step 8.3.1.1.4.2Rewrite the expression.Step 8.3.1.1.5Evaluate the exponent.Step 8.3.1.2Rewrite as .Tap for more steps...Step 8.3.1.2.1Use to rewrite as .Step 8.3.1.2.2Apply the power rule and multiply exponents, .Step 8.3.1.2.3Combine and .Step 8.3.1.2.4Cancel the common factor of .Tap for more steps...Step 8.3.1.2.4.1Cancel the common factor.Step 8.3.1.2.4.2Rewrite the expression.Step 8.3.1.2.5Evaluate the exponent.Step 8.3.1.3Add and .Step 8.3.2Combine and into a single radical.Step 8.3.3Divide by .Step 9Find the focal parameter.Tap for more steps...Step 9.1Find the value of the focal parameter of the hyperbola by using the following formula.Step 9.2Substitute the values of and in the formula.Step 9.3Simplify.Tap for more steps...Step 9.3.1Rewrite as .Tap for more steps...Step 9.3.1.1Use to rewrite as .Step 9.3.1.2Apply the power rule and multiply exponents, .Step 9.3.1.3Combine and .Step 9.3.1.4Cancel the common factor of .Tap for more steps...Step 9.3.1.4.1Cancel the common factor.Step 9.3.1.4.2Rewrite the expression.Step 9.3.1.5Evaluate the exponent.Step 9.3.2Multiply by .Step 9.3.3Combine and simplify the denominator.Tap for more steps...Step 9.3.3.1Multiply by .Step 9.3.3.2Raise to the power of .Step 9.3.3.3Raise to the power of .Step 9.3.3.4Use the power rule to combine exponents.Step 9.3.3.5Add and .Step 9.3.3.6Rewrite as .Tap for more steps...Step 9.3.3.6.1Use to rewrite as .Step 9.3.3.6.2Apply the power rule and multiply exponents, .Step 9.3.3.6.3Combine and .Step 9.3.3.6.4Cancel the common factor of .Tap for more steps...Step 9.3.3.6.4.1Cancel the common factor.Step 9.3.3.6.4.2Rewrite the expression.Step 9.3.3.6.5Evaluate the exponent.Step 9.3.4Cancel the common factor of and .Tap for more steps...Step 9.3.4.1Factor out of .Step 9.3.4.2Cancel the common factors.Tap for more steps...Step 9.3.4.2.1Factor out of .Step 9.3.4.2.2Cancel the common factor.Step 9.3.4.2.3Rewrite the expression.Step 10The asymptotes follow the form because this hyperbola opens left and right.Step 11Simplify .Tap for more steps...Step 11.1Add and .Step 11.2Multiply by .Step 12Simplify .Tap for more steps...Step 12.1Add and .Step 12.2Rewrite as .Step 13This hyperbola has two asymptotes.Step 14These values represent the important values for graphing and analyzing a hyperbola.Center: Vertices: Foci: Eccentricity: Focal Parameter: Asymptotes: , Step 15

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