SOLUTION: 6. Determine the equation in vertex form for the following equation. Vertex = (-1,6) Points = (0,4) 7. Graph the equation in Desmos or Geogebra. Then answer the following qu

Question 1198798: 6. Determine the equation in vertex form for the following equation.
Vertex = (-1,6)
Points = (0,4)
7. Graph the equation in Desmos or Geogebra. Then answer the following questions. A person throws a ball straight up in the air. The height of a ball, h, in meters, can be modelled by h=-4.9t2+10.78t+1.071, where t is the time in seconds since the ball was thrown.
a) What is the maximum height the ball can reach?

b) How tall is the person that throws the ball up in the air?

c) If the thrower also wants to catch the ball, what time do you think that will occur at?

d) What is an appropriate domain and range for this situation? Explain why you chose these parameters.

Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
we use the vertex form equation.
f(x) = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex.
Given the vertex (-1, 6), we substitute the values into the equation:
f(x) = a(x - (-1))^2 + 6
Simplifying further:
f(x) = a(x + 1)^2 + 6
using the given point (0, 4).
Substitute x and f(x) into the equation:
4 = a(0 + 1)^2 + 6
4 = a(1)^2 + 6
4 = a + 6
a = -2
substitute 'a' back into the equation:
f(x) = -2(x + 1)^2 + 6
So, the equation in vertex form is f(x) = -2(x + 1)^2 + 6.
.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The response from the other tutor uses the given vertex and the given other point, along with the vertex form of the equation, to determine the coefficient "a":

------------------------------------------------------------------
we use the vertex form equation.
f(x) = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex.
Given the vertex (-1, 6), we substitute the values into the equation:
f(x) = a(x - (-1))^2 + 6
Simplifying further:
f(x) = a(x + 1)^2 + 6
using the given point (0, 4).
Substitute x and f(x) into the equation:
4 = a(0 + 1)^2 + 6
4 = a(1)^2 + 6
4 = a + 6
a = -2
------------------------------------------------------------------------

If you have a good understanding of the vertex form of the equation of a parabola, then you can find the coefficient "a" with much less work using this shortcut.

The other given point is 1 unit to the right of the vertex. The value 1 unit to the right of the vertex will differ from the value at the vertex by a(1^2) = a. Since the value at the other point is 2 less than the value at the vertex, the coefficient "a" is -2.

Once you have found the value of "a", then continue as the other tutor does to find the equation in vertex form is

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