SOLUTION: I am in my last few weeks of my algebra class and it is getting really hard for me can someone please help me solve these problems? 1. For the first part of this worksheet, we�ll

Question 596109: I am in my last few weeks of my algebra class and it is getting really hard for me can someone please help me solve these problems?
1. For the first part of this worksheet, we�ll be looking at the equation
y = -16x� + 368x + 144
(a) +Does the graph of this equation open up or down? How do you know?
(b) Describe the shape of the graph.
(c) Will the graph of y = -16x� + 368x + 144 reach a maximum or a minimum?
(d) Find the x-coordinate of the vertex. Show your work!
(e) Find the y-coordinate of the vertex. Show your work!
(f) Find the discriminant for the equation -16t2 + 368t + 144 = 0
(g) How many solutions are there to the equation from part (f)? How do you know?
NOTE: You will find the solution(s) in part (h). In this part, you are just supposed to think about how many solutions there will be without finding the solutions first.
(h) Use the quadratic formula to determine solution(s) to the equation in (f). Give the exact solutions, in simplified form. Show your work!
(i) Find the decimal approximations for the solutions you found in (h).
My answers:
(a) The graph would open up because the equation is positive.
(b) The graph would be U shaped.
(c) Maximum
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. For the first part of this worksheet, we�ll be looking at the equation
y = -16x� + 368x + 144
(a) +Does the graph of this equation open up or down? How do you know?
The coefficient of the x^2 term is negative, so it opens downward.
----------------
(b) Describe the shape of the graph.
It's a parabola.
--------------
(c) Will the graph of y = -16x� + 368x + 144 reach a maximum or a minimum?
It has a max, due to part (a).
--------------
(d) Find the x-coordinate of the vertex.
The LOS (Line of Symmetry) is x = -b/2a
x = -368/-32
x = 11.5
---------------
(e) Find the y-coordinate of the vertex.
f(11.5) = -16*11.5^2 + 368*11.5 + 144
= 2260
(f) Find the discriminant for the equation -16t2 + 368t + 144 = 0
Disc = b^2 - 4ac = 368^2 -4*-16(144)
Disc = 144640
------------------
(g) How many solutions are there to the equation from part (f)?
The Disc > 0 --> 2 real solutions.
-------------------
(h) Use the quadratic formula to determine solution(s) to the equation in (f). Give the exact solutions, in simplified form.

(i) Find the decimal approximations for the solutions you found in (h).
x = 23.385
x = -0.385
========================================
My answers:
(a) The graph would open up because the equation is positive.
(b) The graph would be U shaped.
(c) Maximum
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