Solving Quadratic Equations
Quadratic equations have an x-squared term and create parabola-shaped graphs.
Core Concept
A quadratic is ax^2+bx+c=0. Methods to solve: FACTORING x^2+5x+6=0 becomes (x+2)(x+3)=0, x=-2 or x=-3. QUADRATIC FORMULA: x=(-b +/- sqrt(b^2-4ac))/(2a). COMPLETING THE SQUARE rearranges to vertex form. The DISCRIMINANT b^2-4ac tells how many solutions: positive=2 real, zero=1 real, negative=0 real (2 complex). Parabolas open up if a>0, down if a<0.
Examples
x^2-9=0: x=+/-3. x^2+5x+6=0: (x+2)(x+3)=0, x=-2,-3. 2x^2-8=0: x=+/-2.
Solve x^2 - 16 = 0
Going Deeper
Every quadratic has at most 2 solutions. The graph crosses the x-axis at each solution.
Parabola Gallery
Graph y=x^2, y=2x^2, y=-x^2, and y=x^2+3. Describe how a and c affect the shape.
Factor Race
List 10 quadratics to factor. First person to correctly factor all 10 wins!
The quadratic formula uses what under the square root?
A parabola opens downward when?
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