Am I right?
Consider the function y=x^2+5x-2. What would happen to the graph if (x - 3) was substituted in place of the x?
A. The graph would shift up 3 units.
B. The graph would shift down 3 units.
C. The graph would shift 3 units to the right. <---
D. The graph would shift 3 units to the left.
Eq1: Y = x^2 + 5x - 2
h = -B/2A = -5/2
k = (-5/2)^2 + 5*(-5/2) - 2 = 25/4 - 25/2 - 2 = 25/4 - 50/4 - 8/4 = -33/4
V(-5/2, -33/4)
Y = (x-3)^2 + 5(x-3) - 2
Eq2: Y = x^2 - x - 8
h = -B/2A = 1/2
k = (1/2)^2 - 1/2 - 8 = -8 1/4 = -33/4
V(1/2, -33/4).
D. Shifted 3 units to the right.
Hmm, let me put on my clown nose and entertain you with an answer!
Well, if you substitute (x - 3) in place of x, it would be like saying "Hey, Mr. Graph, can you take a little stroll to the right and have a nice cup of tea at the x = 3?". So, I'd say the correct answer is C. The graph would shift 3 units to the right. Now, don't forget to bring your clown wig when you go graphing - it makes all the difference!
To determine what would happen to the graph of the function y=x^2+5x-2 if (x - 3) was substituted in place of x, we can follow these steps:
1. Substitute (x - 3) in place of x in the original function:
y = (x - 3)^2 + 5(x - 3) - 2.
2. Simplify the equation:
y = (x^2 - 6x + 9) + 5x - 15 - 2.
3. Combine like terms:
y = x^2 - x - 8.
Comparing this simplified equation to the original function y = x^2 + 5x - 2, we can see that the graph has shifted to the right by 3 units. Therefore, the correct answer is C. The graph would shift 3 units to the right.
To determine the effect of substituting (x - 3) in place of x in the function y = x^2 + 5x - 2, you can start by replacing x with (x - 3) in the function:
y = (x - 3)^2 + 5(x - 3) - 2
Next, you can simplify the expression:
y = x^2 - 6x + 9 + 5x - 15 - 2
= x^2 - x - 8
Comparing this new expression, y = x^2 - x - 8, with the original function y = x^2 + 5x - 2, you can see that the graphs are not similar.
Therefore, by substituting (x - 3) in place of x, the graph of the function would shift 3 units to the right.
So the correct answer is C. The graph would shift 3 units to the right.