Solutions, Zeros, and Roots Quadratic Function Solutions, Zeros, and Roots

Quadratic Function (y = ax2 + bx + c) a, b, and c are called the coefficients. The graph will form a parabola. Each graph will have either a maximum or minimum point. There is a line of symmetry which will divide the graph into two halves.

Solving Quadratic Functions (ax2 + bx + c = 0) Since y = ax2 + bx +c , by setting y=0 we set up a quadratic equation. If we set y = 0, we can use different methods to find the solutions. The easiest way is by graphing.

To solve quadratic equations (graphing method) X2 - 2x = 0 To solve the equation, put y1 = x2-x into your calculator. Put y2 = 0 Find the x intercept by using intersection. Two solutions, x=0 and x=2. y=x2-2x

Find the Solutions x2-4 = 0 x2+2x-15 = 0 -x2+5 = 0 -x2-1 = 0

Find the roots y=-x2+4x-1 y=x2+2x+1

Observations Sometimes there are two solutions. Sometimes there is only one solution. Sometimes it is hard to locate the solutions. Sometimes there is no solution at all.

Other Methods By factoring By using the quadratic formula

More Practice 8x2 – 15x – 5 = -3 x2 - 2x - 48 = 0 x2 + 3x = 28

The End