Question

PLEASE ANSWER...

We first started looking at equations such as y=x^2 + 5 but NOW we are looking at v? equations such as y= (x + 5)^2. What is the difference in the way that the EQUATIONS look? Does this affect the graph?!

Option 1: The first equation is quadratic, and the second equation is a shifted quadratic.
Option 2: The first equation is linear, and the second equation is quadratic.
Option 3: The first equation is quadratic, and the second equation is linear.
Option 4: The equations look the same, and they have the same graph but shifted.

Answer 1

The difference in the way the equations look is that the first equation is a quadratic, while the second equation is a shifted quadratic. The graph of the second equation will be shifted horizontally to the left compared to the graph of the first equation.

Step-by-step explanation:

The difference in the way the two equations, y = x^2 + 5 and y = (x + 5)^2, look is that the first equation is quadratic, while the second equation is a shifted quadratic. The first equation has the form y = ax^2 + bx + c, where a, b, and c represent constants. The second equation is a quadratic equation with the form y = a(x - h)^2 + k, where (h, k) represents the vertex or the point of translation.

The first equation represents a parabola with the vertex at the origin (0, 0), while the second equation represents a parabola that has been shifted 5 units to the left. This means that the graph of the second equation will be shifted horizontally to the left compared to the graph of the first equation.

In summary, Option 1 is correct: The first equation is quadratic, and the second equation is a shifted quadratic.