# Welcome to Algebra I: Finding Zeros of Quadratic Functions

13 minutes

Hey, guys. Welcome to Algebra 1. Today we're going to focus on finding zeroes of quadratic functions. Your knowledge of factoring and the coordinate plane and x-intercepts will come in handy during this lesson. You ready to get started? Let's go.

(negative 5, 0) and (4, 0). There you go-- you've got your zeroes for this quadratic function. Okay? Let's try another one. Here we're asked to find the zeroes of the quadratic function, y equals x squared minus 3x minus 10. Okay? Again, when you're asked to find the zeroes, you're really being asked to find the x-intercepts. Those are interchangeable terms. For my x-intercept, I always like to write myself a little hint that the x value is some numerical value, but y must be 0. To find the zeroes of this function, I'm going to start out by replacing that y with a 0. So, I'll have 0 equals x squared minus 3x minus 10. Then I'm going to get this right side factored, to solve this quadratic. I'm looking for two numbers that have a product of negative 10, but when added together, they get negative 3. For this case it's going to be negative 5 and positive 2. Because negative 5 times positive 2 is negative 10, and negative 5 plus positive 2-- or negative 5 plus 2-- is negative 3. Okay? Let's rewrite that right side:

(x minus 5) and (x plus 2). And then let's solve these two-- what I like to call mini equations-- two one-step equations, to get exactly the value of each of those x-intercepts. We'll have x minus 5 equals 0, and we'll have x plus 2 equals 0. So we'll add 5 to each side here. Okay? So, that'll wipe out, And x equals 5 is one of my zeroes. Then I'll subtract 2, subtract 2 over here. And x equals negative 2 is my other zero. Now if I want, I could stop here. This is an acceptable answer. My zeroes are at x equals 5 and negative 2. Or I could also write these as ordered pairs. I could represent them as (5, 0) and-- let's get a little more room here--

(negative 2, 0). Either way is fine. Okay. All right? I do believe it's time for you to try one. Press pause. Take a few minutes. And find the zeroes of this quadratic function. To compare your answers against mine, press play.

(female narrator) Find the zeroes of the quadratic function: y equals x squared minus 7x plus 12. All right, let's see how you did. First, if I'm being asked to find the zeroes, I know I'm being asked to find the x-intercepts. And I know those always take the form of x as some number, y is 0. So to find the zeroes of this quadratic, I'll start out by replacing y with 0. So 0 equals x squared minus 7x plus 12. Now I have a quadratic equation, and in order to solve it, what I'm going to do is get that right side factored. I need two numbers that have a product of positive 12 but a sum of negative 7. Going through the factors, you'll find that it is negative 4 and negative 3. Because negative 4 times negative 3 is positive 12, and negative 4 plus negative 3 is negative 7. Let's rewrite this right side as a product of factors.

(female narrator) The bottom of the parabola is just under the x-axis and crosses the x-axis at 1 and 2. All right? Let's see how you did. Let me get my graph locked in place here so it doesn't start to move on me. Let's locate these zeroes. If I'm asked to find the zeroes, I'm really finding the x-intercepts. And I have one located right here, and another right there. I'm just going to write those locations as ordered pairs. So, I have (1, 0) right here at 1, 0, believe it or not. And I have another zero located right here at (2, 0). There are the locations of my two zeroes for my quadratic function. All right, great job, guys, finding the zeroes of your quadratic functions. I hope you saw how factoring and your knowledge of the coordinate plane came in handy for this lesson. Hope to see you back here soon for more Algebra 1. Bye!

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In this program, students learn how to find the zeros of quadratic functions. These points occur where the graph of the quadratic equation crosses the x-axis. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 13 minutes