10.3 Solving Quadratic Equations

10.3 – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using square roots

10.3 – Solving Quadratic Eq. When you look at a parabola, there are many important things to consider.  Vertex  Line of symmetry  y-intercept

10.3 – Solving Quadratic Eq. MOST IMPORTANT But one of the MOST IMPORTANT parts of the graph is where it crosses the x- axis or the x-intercept.

10.3 – Solving Quadratic Eq. quadratic equation To find the x-intercept, we use the quadratic equation. ax + bx + c = 0 When you solve this equation, you will see 0, 1, or 2 solutions to the equations. What do I mean by this? 2

10.3 – Solving Quadratic Eq. “0” solutions

10.3 – Solving Quadratic Eq. “1” solutions

10.3 – Solving Quadratic Eq. “2” solutions

10.3 – Solving Quadratic Eq. The x-intercept is also called the root OR zeros. To find the zeros we can graph or solve the equations.

x y O roots 10.3 – Solving Quadratic Eq.

Solve x 2 = 8 algebraically. 1 2 Check your solution graphically. 1 2 x 2 = 8 S OLUTION Write original equation. x 2 = 16 Multiply each side by 2. Find the square root of each side. x =  4 Check these solutions using a graph. C HECK 10.3 – Solving Quadratic Eq.

Write the equation in the form ax 2 + bx + c = x 2 = 8 Rewrite original equation. 1 2 x 2 – 8 = 0 Subtract 8 from both sides. y = 1 2 x 2 – 8 Write the related function y = ax 2 + bx + c. 1 2 Check these solutions using a graph. C HECK 10.3 – Solving Quadratic Eq.

2 3 Check these solutions using a graph. Sketch graph of y = 2 x 2 – 8. 1 The x-intercepts are  4, which agrees with the algebraic solution. Write the related function y = 1 2 x 2 – 8 y = ax 2 + bx + c. C HECK 4, 0– 4, – Solving Quadratic Eq.

Solve x 2 – x = 2 graphically. Check your solution algebraically. S OLUTION ax 2 + bx + c = 0 Write the equation in the form ax 2 + bx + c = 0 x 2 – x = 2 Write original equation. x 2 – x – 2 = 0 Subtract 2 from each side. Write the related function y = ax 2 + bx + c. y = x 2 – x – – Solving Quadratic Eq.

Write the related function y = ax 2 + bx + c. y = x 2 – x – 2 Sketch the graph of the function y = x 2 – x – 2 From the graph, the x-intercepts appear to be x = –1 and x = – 1, 0 2, – Solving Quadratic Eq.

From the graph, the x-intercepts appear to be x = –1 and x = 2 You can check this by substitution. Check x = –1: Check x = 2: x 2 – x = 2 (–1) 2 – (–1) 2 = ? = 2 x 2 – x = 2 4 – 2 = – 2 = 2 ? – 1, 0 2, 0 C HECK 10.3 – Solving Quadratic Eq.

We can also find the zeroes by using a special function on our calculators. So……..synchronize your calculators!!!

10.3 – Solving Quadratic Eq. graph x – 1 = 02x + 4 = 0 22

10.3 – Solving Quadratic Eq. Solve: 3x + 12 = 12 2

10.3 – Solving Quadratic Eq. Solve: x – 25 = 0 2