Final answer:
The x-intercepts of the graph f(x) = x² - 4x - 21 are x = 7 and x = -3. These are found by factoring the quadratic equation and solving for x.
Step-by-step explanation:
To determine the x-intercepts of the graph f(x) = x² - 4x - 21, we need to find the values of 'x' where the function value (f(x)) is zero. The x-intercept is where the graph crosses the x-axis. We can find the x-intercepts by setting f(x) to zero and solving the equation for x. This is a quadratic equation, and it can be solved using factorization or the quadratic formula.
First, try to factor the equation:
- Find two numbers that multiply to give -21 and add to give -4 (the coefficient of x).
- The numbers that satisfy this are -7 and 3 because (-7) * 3 = -21 and (-7) + 3 = -4.
- Therefore, the factored form of the equation is (x - 7) * (x + 3) = 0.
- To find the solutions, set each factor equal to zero: x - 7 = 0 or x + 3 = 0.
- Solving these two equations gives us the x-intercepts: x = 7 or x = -3.