1. Quadratic functions: related to parabolas

1) Given a quadratic function y = 2x^2 - 6x + 7, find the coordinates of the vertex by using the method of completing the square.

2) A stone was thrown vertically upwards from the ground. Its height above the ground, s meters, reached in t seconds was given by
s = -5t^2 + 40t

a) Express s in the form a(t - b)^2 + c, where a, b and c are constants.
b) What is the greatest height reached and the time to obtain this height?

2. Originally Posted by BG5965
1) Given a quadratic function y = 2x^2 - 6x + 7, find the coordinates of the vertex by using the method of completing the square.

Mr F says: ${\color{red}y = 2\left(x^2 - 3x + \frac{7}{2}\right)}$. So complete the square on ${\color{red}x^2 - 3x + \frac{7}{2}}$ (see below) and then multiply the result the result by 2.

2) A stone was thrown vertically upwards from the ground. Its height above the ground, s meters, reached in t seconds was given by
s = -5t^2 + 40t

a) Express s in the form a(t - b)^2 + c, where a, b and c are constants.

Mr F says: ${\color{red}y = -5\left(t^2 - 8t\right)}$. So complete the square on ${\color{red}t^2 - 8t}$ (see below) and then multiply the result the result by -5.

b) What is the greatest height reached and the time to obtain this height?

Mr F says: y-coordinate of turning point and t-coordinate of turning point.