Question

Multiply (x-7)(x+3) and use this product to identify the y-intercept of the graph of f.

(PLEASE do step by step and tell me what to write i need to show my work)

Answer 1

Answer:

Here you go

Step-by-step explanation:

Sure, let's multiply (x - 7)(x + 3) step by step using the distributive property:

1. First, we'll multiply the terms in the first set of parentheses by the terms in the second set of parentheses:

  (x - 7)(x + 3) = x(x) + x(3) - 7(x) - 7(3)

2. Next, we'll simplify each term:

  = x^2 + 3x - 7x - 21

3. Combine like terms:

  = x^2 - 4x - 21

So, the product of (x - 7)(x + 3) is x^2 - 4x - 21.

Now, to identify the y-intercept of the graph of f, we need to find where the graph intersects the y-axis, which occurs when x = 0.

To find the y-intercept, substitute x = 0 into the function:

f(0) = 0^2 - 4(0) - 21

     = 0 - 0 - 21

     = -21

Therefore, the y-intercept of the graph of f is -21.

Answer 2

Sure, let’s go through the step-by-step solution:

Multiply the two binomials:

(x - 7)(x + 3)

To do this, we need to use the distributive property. We multiply each term in the first parentheses with each term in the second parentheses:

x(x + 3) - 7(x + 3)

Simplify the expression:

x(x + 3) - 7(x + 3)

x^2 + 3x - 7x - 21

Combine like terms:

x^2 + 3x - 7x - 21

x^2 - 4x - 21

This is the product of the two binomials (x - 7)(x + 3).

Now, to identify the y-intercept of the graph of the function f(x) = x^2 - 4x - 21, we need to find the value of f(x) when x = 0.

Substituting x = 0 into the function:

f(0) = 0^2 - 4(0) - 21

f(0) = -21

Therefore, the y-intercept of the graph of f(x) = x^2 - 4x - 21 is -21.