Answer:
Explanation:
To find the zeros of the function f(x) = -3x² + 75, we need to solve the equation -3x² + 75 = 0 for x. We can start by factoring out a common factor of -3:
-3x² + 75 = 0
-3(x² - 25) = 0
Now we can use the difference of squares formula to factor the expression inside the parentheses:
-3(x - 5)(x + 5) = 0
This equation is satisfied when one of the factors is equal to zero, so we can set each factor equal to zero and solve for x:
x - 5 = 0 --> x = 5
x + 5 = 0 --> x = -5
Therefore, the zeros of the function are x = -5 and x = 5, and we can write them in order from least to greatest as:
lesser x = -5
greater x = 5
Calculator solution:
To verify these results using a calculator, you can graph the function y = -3x² + 75 and look for where the graph intersects the x-axis. Here's how you can do that on a TI-84 calculator:
1) Press the "Y=" button to enter the function.
2) Enter "-3x^2 + 75" after "Y1=".
3) Press the "GRAPH" button to see the graph.
4) Press the "2nd" button followed by the "CALC" button (which is the "TRACE" button).
5) Select option 2: "zero" by pressing the number 2 on the calculator or using the arrow keys to highlight it and pressing "ENTER".
6) Move the cursor to the left of the zero on the left side of the graph and press "ENTER".
7) Move the cursor to the right of the zero on the right side of the graph and press "ENTER".
8) The calculator will display the zeros and ask if you want to store them to a variable. You can simply write down the values and press "ENTER" twice to exit the calculator's calculation.
The calculator will confirm that the zeros are x = -5 and x = 5, as we found above.