unit 5 lesson 10 quadratic functions and equations unit test part 1
17 questions, plz give first 16 answers
The graph of y=x^2 is shown below
which of the following graphs could be the graph of y=x^2-3
1. "Well, I would say that the graph that looks like a sad parabola frowning slightly downwards could be the graph of y = x^2 - 3. It's feeling a bit down, you know? But hey, at least it's still a parabola!"
2. "Imagine you have a graph of y = x^2, and then you take that graph and move it three units down. Voila! You've got yourself the graph of y = x^2 - 3. So look for a parabola that's shifted downwards, like it's going through a minor existential crisis."
3. "Think of it this way: the graph of y = x^2 is like a happy parabola, bouncing around and having a good time. Now, imagine you take away three units of happiness from that parabola. What do you get? A slightly sadder parabola, still bouncing, but with a slight frown. That's the graph of y = x^2 - 3."
4. "Picture a parabola with its head held high, in the form of y = x^2. Now, imagine something happens to it, and it gets three units of depression. It'll start drooping a bit, right? That's exactly what the graph of y = x^2 - 3 looks like. Poor parabola, it needs a hug."
5. "If the graph of y = x^2 is like a smiley parabola, then the graph of y = x^2 - 3 is like a slightly less smiley parabola. It's still hanging on, though! Just feeling a bit down, maybe in need of a good joke or two."
To determine which of the following graphs could be the graph of y=x^2-3, we need to understand how this equation affects the original graph of y=x^2.
The equation y=x^2-3 is a quadratic function that shifts the graph of y=x^2 downward by 3 units. This means that every point on the graph of y=x^2-3 will be 3 units below the corresponding point on the graph of y=x^2.
Now let's examine the given answer choices and choose the graphs that meet this condition.
1. The graph is the same as y=x^2 but shifted downward by 3 units. This could be the graph of y=x^2-3.
2. The graph appears to be shifted upward, not downward. This is not the correct choice.
3. The graph appears to be a straight line, not a curve. This is not the correct choice.
4. The graph appears to be flipped upside down. This is not the correct choice.
5. The graph appears to be shifted to the left, not downward. This is not the correct choice.
Therefore, the correct answer choices for the graphs that could be the graph of y=x^2-3 are 1.