There are a couple of ways to "consider" factoring these. They stem from:

**y = ax^2 + bx + c**

The general form for a quadratic equation, the form your equation is written in, with:

**a = 1. b = -2, and c = -15**

I will assume your teacher is working with the "easier method" first, when **a = 1**.

You are looking for two parenthesis of the form when you factor this:

**(x + #)(x + #)**, both numbers can be different, even positive and negative.

When a = 1, then the method calls for trying to determine 2 numbers that multiply to c but add to b. So, in this case:

**two number that multiply to -15 and add to -2**

Start considering all the factors for -15:

5*-3

-5*3

1*-15

-1*15

There are no other pairs of numbers. The question, which pair of numbers, when you add them together, gives you -2? **The -5 and 3:**

**-5*3 = -15**

**-5 + 3 = -2**

So, from there, you just plug them into (x+#)(x+#):

x^2 - 2x - 15 = (x + -5)(x + 3) = (x - 5)(x + 3)

So, we have:

**y = (x - 5)(x + 3)**

To find the horizontal intercepts, or the x intercepts, **you are setting each parenthesis = 0** and solving for x:

**x-5 = 0 and x + 3 = 0**

So, **x = 5 and -3**

So, the graph would cross the x axis at **(5,0) and (-3,0)**

The equation `h(z)=z^2-2z-15` is easily factored. Two factors of 15 with a difference of 2 are: 5 and 3. Since the second coefficient is negative, then the 5 has to be negative to get both coefficients to be negative. The factored function is `h(z)=(z+3)(z-5)`

I infer from the second half of the question that they mean h(z)=y and z=x, and the horizontal intercepts are the x-intercepts i.e. where the graph of the function crosses the x-axis or y=0 There are exactly two coordinates where this happens, and in the ascending order of x values they are (-3,0) and (5,0).

You can verify by plugging the first number of each ordered pair in for z and finding that the computed value for h(z) is 0 (the second number in each ordered pair).

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now