Solving Problems Involving Quadratic Relations

Solve the following problems involving quadratic relations. You can choose to do so algebraically or graphically. If you choose to solve it graphically, you must attach a rough sketch of the graph from Desmos. If you choose to solve algebraically, SHOW ALL OF YOUR WORK.

A weight was dropped from a platform. Its path can be modelled by the equation h=−4.9t^2+13, where h represents the height of the ball in meters and t represents the time in seconds.
a) What is the height of the platform?
b) How long did it take the ball to land? 

Graphing Quadratic Relations Algebraically
Graph the following quadratic relations algebraically by finding each of the key features listed.

x^2−5 x+4
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−5 x+6
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−x−6
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−10 x+25
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

A.Solve the following algebraic expressions;

(i) y- 13 = 15- 2y

(ii) 12x -4 = 14 +10x

Solve the following Quadratic Equations by Factorization:

(iii) x2 + 5x – 14 = 0

(iv) x2 +3x – 4 = 0