9.2 Solving Quadratic Equations by Graphing Algebra 1 9.2 9.2 Solving Quadratic Equations by Graphing One option for solving quadratic equations is to do it by graphing. The solution or solutions of the quadratic equation are called roots. You find the roots by finding the x-intercepts of the graph (also called zeros). So we call solutions: Solutions, roots, x-intercepts, or zeros…all mean the same thing.

You can have 0,1, or 2 roots to any quadratic equation. 0 – never crosses the x-axis 1 – vertex is on the x-axis (double root) 2 – crosses the x-axis 2 times When told to “solve” – you have to figure out how many roots there are and where they cross the x-axis.

Solve x2 – 6x = -9 Get it to = 0 by adding 9 to both sides. Where is the axis of symmetry? Where is the vertex? Pick two points to the right Reflect them across the axis of symmetry. Draw parabola. The graph sits on the x-axis so there is only one root and it is at the vertex. {3}

The graph never crosses the x-axis so there is no solution. Solve x2 + 2x + 3 = 0 x2 + 2x + 3 = 0 Where is the axis of symmetry? Where is the vertex? Pick two points to the right Reflect them across the axis of symmetry. Draw parabola. The graph never crosses the x-axis so there is no solution.

The graph crosses the x-axis between -4 & -3 and also between -1 & 0 Solve -2x2 – 8x – 2 = 0 -2x2 - 8x – 2 = 0 Where is the axis of symmetry? Where is the vertex? Pick two points to the right Reflect them across the axis of symmetry. Draw parabola. The graph crosses the x-axis between -4 & -3 and also between -1 & 0

Determine the number of roots by factoring. f(x) = x2 + 7x + 12 f(x) = (x + 4)(x + 3) if set = 0…x = -4, x = -3; thus, this function would have 2 roots…one at -4 & one at -3 f(x) = x2 – 16x + 64 f(x) = (x – 8)2 if set = 0…x = 8; we call this a double root; thus, this function would have 1 root at 8.

Homework #64 p. 483 12-30 (x 3’s), 45