Answer:
f(x) = x² - 2x - 15 passes through (-3 , 0) , (0 , -15) , (5 , 0)
f(x) = -x² - 2x + 15 passes through (-2 , 15) , (-1 , 16) , (0 , 15)
f(x) = -x² + 2x - 15 passes through (0 , -15) , (1 , -14) , (2 , -15)
Step-by-step explanation:
* Lets explain how to solve this question
- To find the points whose graph passes through them substitute the
x-coordinate in the function if the answer is the same with the
y-coordinate of the point then the graph passes through this point
lets do that
- Check the first set of points with the first function
# Pint (0 , -15)
∵ f(x) = x² - 2x - 15
∴ f(0) = (0)² - 2(0) - 15 = -15 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (0 , -15)
# Pint (1 , -14)
∵ f(x) = x² - 2x - 15
∴ f(0) = (1)² - 2(1) - 15 = -16 ⇒ not same value of y-coordinate
∴ The graph of the function does not pass through point (1 , -14)
∴ The graph does not pass through this set of points
- Check the second set of points with the first function
# Pint (-2 , 15)
∵ f(x) = x² - 2x - 15
∴ f(0) = (-2)² - 2(-2) - 15 = 4 + 4 - 15 -7 ⇒ not same value of y-coordinate
∴ The graph of the function does not pass through point (-2 , 15)
∴ The graph does not pass through this set of points
- Check the third set of points with the first function
# Pint (-3 , 0)
∵ f(x) = x² + 2x - 15
∴ f(0) = (-3)² - 2(-3) - 15 = 9 + 6 -15 = 0 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (-3 , 0)
# Pint (0 , -15)
∵ f(x) = x² - 2x - 15
∴ f(0) = (0)² - 2(0) - 15 = -15 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (0 , -15)
# Pint (5 , 0)
∵ f(x) = x² + 2x - 15
∴ f(0) = (5)² - 2(5) - 15 = 25 - 10 -15 = 0 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (5 , 0)
∴ The graph passes through this set of points
* f(x) = x² - 2x - 15 passes through (-3 , 0) , (0 , -15) , (5 , 0)
- Check the first set of points with the second function
# Pint (0 , -15)
∵ f(x) = -x² - 2x + 15
∴ f(0) = -(0)² - 2(0) + 15 = 15 ⇒ not same value of y-coordinate
∴ The graph of the function does not passes through point (0 , -15)
∴ The graph does not pass through this set of points
- Check the second set of points with the second function
# Pint (-2 , 15)
∵ f(x) = -x² - 2x + 15
∴ f(0) = -(-2)² - 2(-2) + 15 = -4 + 4 + 15 = 15 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (-2 , 15)
# Pint (-1 , 16)
∵ f(x) = -x² - 2x + 15
∴ f(0) = -(-1)² - 2(-1) + 15 = -1 + 2 + 15 = 16 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (-1 , 16)
# Pint (0 , 15)
∵ f(x) = -x² - 2x + 15
∴ f(0) = -(0)² - 2(0) + 15 = 15 ⇒ same value of y-coordinate
∴ The graph of the function passes through point (0 , 15)
∴ The graph passes through this set of points
* f(x) = -x² - 2x + 15 passes through (-2 , 15) , (-1 , 16) , (0 , 15)
- Now we have the first set of points and the third function
∴ The graph passes through this set of points
∴ f(x) = -x² + 2x - 15 passes through (0 , -15) , (1 , -14) , (2 , -15)