4. What are the zeroes of y = x^2 + 2x – 8? (1 point) -4, 2 4, 2 -4,2 4, 2
2 answers:
Answer:
x=-4, x=2
Step-by-step explanation:
Whenever a question asks you to find the zeros of a quadratic equation, they are essentially asking you to find the x-intercepts. To find the x-intercepts, you simply need to equate y to zero and solve for x.
There are two main ways to find the intercepts - by the quadratic formula and factoring. I will demonstrate both below.
When factoring, a popular method is the diamond box method. First, make an x on your paper. In the top nook of the x, write the product of a and c in y=ax^2 +bx +c. Here, it is -8*1=-8. In the bottom nook, write the b value. Here it is 2. Find two numbers that multiply to ac or -8 and add up to b or 2 and write them in the side nooks. In this problem, they are 4 and -2 (4*-2=-8 and 4+(-2)=2). Then, make a box. On the top left corner, write the first term (here it is x^2) and on the bottom right corner write the constant term (here it is -8) and write the two values you found earlier in the remaining boxes. Now, find values that multiply to each of the respective terms. Sorry, this sounds super confusing, I have included a picture below of what the result should look like. Once you have it factored, make y equal to zero and solve for both x's. You should get x=2 and x=-4. Keep in mind, sometimes, a problem might not be factorable. If it isn't, you have to use the method below.
Another popular way to find the roots is the quadratic formula. I have included a picture of it below. All you have to do is substitute the coefficients in and solve for x. You should get two solutions in this scenario.
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