A factored form of x 2 + 5x - 24 is — A (x − 4)(x + 6) B (x − 3)(x + 8) C (x − 2)(x + 12) D (x − 6)(x + 4) Which of the following equals when factored completely? F (3x – 4)(x + 2) G (3x – 1)(x + 8) H (3x + 8)(x − 1) J (3x +2)(x −4) What is that? Well whatever it is… it’s pretty.

a Mr. Warren G classic production

Students will be able to… – Explain what it means to find the solution of a quadratic equation – Identify key words such as solutions, roots, and zeros as associated with quadratics – Use factoring techniques in order to find the solutions of a quadratic equation.

To find x-intercepts of a parabola you can… – Look at the graph and see where the parabola crosses the x-axis – Set y equal to zero and solve for x The x-intercepts of a quadratic function are also referred to as – Solutions – Roots – Zeros

As previously stated solutions, roots, and zeros are all basically key words asking for the same thing… What are the x-intercepts of the quadratic? f (x) = −x 2 − 4x Given the graph of f(x)=-x 2 -4x, what are the x-intercepts of the quadratic function? Given the graph of f(x)=-x 2 -4x, what are the zeros of the quadratic function? Given the graph of f(x)=-x 2 -4x, what are the solutions of the quadratic function?

f (x) = −x 2 − 4x Example The graph of the quadratic function: f (x) = −x 2 − 4x crosses the x-axis at the points (-4, 0) & (0, 0). The solutions, roots, or zeros of the equation are thus: x = -4x = 0 & (6, 0) (4, 0) (-2, 0) (-7, 0) Identify the coordinates of each blue dot on the x-axis. What do you notice about the y-values of each dot on the x-axis? The y-value is 0 for each. Thus, the solutions, roots, or zeros of our quadratics can be identified by: locating the x-intercepts of our parabola, OR…

By setting the standard form quadratic equation y = ax 2 + bx + c f(x) = ax 2 + bx + c equal to zero and solve for x. Why set the quadratic equation equal to zero? We set it equal to zero because anytime we cross the x-axis, the y-value is zero. y = ax 2 + bx + c 0 = ax 2 + bx + c

Types of SOL questions you will see… What are they asking for? Which is a zero of the function defined by the following equation? f (x) = x(x+2) Which number is a zero of the function f ? f ( x ) = x 2 − x − 6 A 0 B 2 C 3 D 6

Now that you understand what we are looking for (solutions, roots, zeros) and how we can find it (where we cross the x-axis, or what x equals when y = 0) you need to learn how to solve a quadratic equation.

If the product of two real numbers a, and b is zero. a · b = 0 then a = 0 or b = 0. Example: (x + 3)(x + 2) = 0 (x + 3) = 0(x + 2) = 0or x = -3x = -2 Both are solutions to the equation (x + 3)(x + 2) = 0

1)(3n − 2)(4n + 1) = 0 4) (n + 2)(2n + 5) = 03) (5n − 1)(n + 1) = 0 2) m(m − 3) = 0

You can also use the Zero-Product Property to solve equations of the form ax 2 + bx + c = 0 if the quadratic expression ax 2 + bx + c can be factored.

1.) x 2 − 11x + 24 = 02.) n 2 + 7n + 10 = 0 3.) 6n 2 − 18n − 24 = 04.) 6b 2 − 13b + 6 = 0

Before solving a quadratic equation, you may need to add or subtract terms in order to write the equation in standard form. – This may also be needed to have our quadratic expression equal to zero. – Our quadratic equal to zero is necessary so we may use the Zero-Product Property. Then factor the quadratic expression and employ the Zero-Product Property

1.) n 2 = −18 − 9n2.) 3k = 33k 3.) 7x 2 = -2x4.) 15a 2 − 3a = 3 − 7a

Remember these? Now answer them. Which is a zero of the function defined by the following equation? f (x) = x(x+2) Which number is a zero of the function f ? f ( x ) = x 2 − x − 6 A 0 B 2 C 3 D 6