Expand (x−7)(x+3) and use the expanded form to identify the y-intercept of the graph of f.

Answer 1

To solve this problem, we need to start by expanding the expression, meaning we multiply (x-7) by (x+3). The most common method for this is FOIL (first, inside, outside, last), but you may be familiar with another technique.

x*x + x*3 + -7*x + -7*3

x² + 3x -7x -21

x² - 4x - 12

So our function can be written as f(x) = x² - 4x - 12. The y-intercept can be found by plugging in 0 as the x-value: f(0) = 0² - 4(0) - 12, so f(0) = -12. The y-intercept, then, is (0, -12). This is always true for an expanded polynomial: the y-intercept is given by the constant usually written at the end of the equation, in this case -12.

Answer 2

(x-7)(x+3) = x^2 -4x -21

y-intercept is when 0 is zero.

when x is zero y is -21