Question

Determine whether or not the following points fall on the graph of f(x) = -3 x² + 6x + 5.

Part A: (3, -4)
Part B: (-1, 4)
Show or explain your work.

Answer 1

A. (3,-4) fall on the graph of f(x) = -3 x² + 6x + 5.

B. (-1,4) DO NOT fall on the graph of f(x) = -3 x² + 6x + 5.

Explanation:

Here, the given function is: f(x) = -3 x² + 6 x + 5

Now, as we know f(x) = y

⇒ y = -3 x² + 6x + 5

Now, to show if any arbitrary point (a,b) is on the graph of y,

we need to show that for y = b, and x = a the Left side of expression =Right side of expression.

A. Consider the point (3,-4)

Here, y = -4, and x = 3

Solving -3 x² + 6 x + 5 for x = 3, we get:

-3 (3)² + 6 (3) + 5 = -27 + 18 + 5 = -27 + 23 = -4 = y

⇒f(3) = y = -4 ⇒ Left Side = Right side

Hence, (3,-4) fall on the graph of f(x) = -3 x² + 6x + 5.

A. Consider the point (-1,4)

Here, y = 4, and x = -1

Solving -3 x² + 6 x + 5 for x = -1, we get:

-3 (-1)² + 6 (-1) + 5 = -3 -6 + 5 = -4 ≠ y

⇒f(-1) = y ≠ 4 ⇒ Left Side≠ Right side

Hence, (-1,4) DO NOT fall on the graph of f(x) = -3 x² + 6x + 5.