Question

Please answer all please​

Answer 1

Answer:

Step-by-step explanation:

The first parabola has vertex (-1, 0) and y-intercept (0, 1).

We plug these values into the given vertex form equation of a parabola:

y - k = a(x - h)^2 becomes

y - 0 = a(x + 1)^2

Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:

1 = a(0 + 1)^2, and from this we know that a = 1.  Thus, the equation of the first parabola is

y = (x + 1)^2

Second parabola:  We follow essentially the same approach.  Identify the vertex and the two horizontal intercepts.  They are:

vertex:  (1, 4)

x-intercepts:  (-1, 0) and (3, 0)

Subbing these values into y - k = a(x - h)^2, we obtain:

                                            0 - 4 = a(3 - 1)^2, or

                                                -4 = a(2)².  This yields a = -1.

Then the desired equation of the parabola is

y - 4 = -(x - 1)^2