Ways to Solve Quadratic Equations

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by tpham17539
Last updated 8 years ago

Algebra I

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Ways to Solve Quadratic Equations

Ways to Solve Quadratic Equations

Square Method1. Put "c" on the other side of the equation.2. Find the coefficient of the x-term and square it.3. Add the squared value to both sides of the equation.4. Factor the equation out into a perfect square.5. Square root both sides of the equation, simplify, and solve.

Quadratic Formula1.Place everything on one side.2.Look at the coefficients and determine a, b, & c.3. Plug them into the quadratic formula.4. Simplify and solve.

Factoring1. Place everything on one side.2. Factor the equation.3. Set the equation equal to 0.4. Solve for each factor.

Graphing1. Put the equation in standard form.2. Find a, b, & c.3. Determine how the parabola opens.4. Find the axis of symmetry with x=-b/2a5. Find the vertex by plugging the axis of symmetry back into the equation.6. Find the y-intercept.7. Graph the vertex and y-intercept. 8. Use the axis of symmetry to find another point on the graph.9. Connect the points and determine the x-intercepts.

Example:2n^2-n-4=2Subtract 2 from both sides.2n^2-n-6=0Factor out the equation.(n-2)(2n+3)=0Solve for each factor.(n-2)=0 OR (2n+3)=0n=2 OR n=-3/2

Example:2n^2-n-4=2Isolate "c".2n^2-n=6Simplify the equation.n^2-.5n=3(.5)/2=.25(.25)^2=.0625Add this value to both sides.n^2-.5n+.0625=3.0625Factor.(n-.25)^2=3.0625Square root both sides.√(n-.25)^2=±√3.0625(n-.25)=±1.75Solve.n=2 OR n=-3/2

Example:2n^2-n-4=2Subtract 2 from each side.2n^2-n-6=0Find a, b, and c.a=2, b=-1, c=-6Plug them into the quadratic formula.x= -(-1)±√(-1)^2 - 4(2)(-6)-----------------------------------------------2(2)Solve for x.x= (1±7)/4x=2 OR x=-3/2

Example:2n^2-n-4=22n^2-n-6=0Find a, b, and c.a=2, b=-1, c=-6The parabola opens up.-(-1)/2(2)=.25Plug this back into the equation.2(.25)^2-(.25)-6-6.125 is the vertex.y-intercept: -6Proceed to the graph and locate the x-intercepts.

The Discriminantb^2-4acIt shows the number of x-intercepts in a quadratic equation.2n^2-n-4=22n^2-n-6=0a=2, b=-1, c=-6(-1)^2-4(2)(-6)1+4849Since it is positive, there are two x-intercepts.

The easiest method was the factoring. It had the least amount of steps and didn't involve any decimals or fractions. This method was very simple to solve.

x= 2 OR x=-3/2

Length: 13 in.Width:7 in.

The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle.

width: x, length: x+6area: length x widthx(x+6)=91x^2 + 6x = 91x^2+6x-91=0(x+13)(x-7)=0The width can't be -13, so it's 7Length: x+67+6=13

Check!l x w=9113 x 7=91✓91=91

By: Tiffany Pham


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