Question

G(r) = (r + 14)² – 49

What are the zeros of the function?
Write the smaller r first, and the larger r
second.
smaller r =
larger r =

Answer 1

The function G(r) factors into (r + 21)(r - 7), leading to zeros at r = -21 and r = 7, where -21 is the smaller zero and 7 is the larger zero.

Step-by-step explanation:

The function provided is a quadratic function, G(r) = (r + 14)² – 49, which can be factored to find its zeros. To factor the expression, we recognize it as a difference of squares, where (r + 14)² is the square of (r + 14) and 49 is the square of 7. Therefore, the function can be written as (r + 14 + 7)(r + 14 - 7), which simplifies to (r + 21)(r - 7).

Setting each factor equal to zero gives us the zeros of the function. For r + 21 = 0, the solution is r = -21, and for r - 7 = 0, the solution is r = 7. Thus, the zeros of the function are r = -21 and r = 7, with -21 being the smaller r and 7 being the larger r.

The zeros of the quadratic function help in graphing the parabola and also indicate the r-values where the function will cross the r-axis on a graph.