Find the vertex and axis of symmetry of y = -2x^2 + 4x + 1. Show all of your work and justify your reasoning.

Question

Note: The ^ symbol means to the power.

Answer 1

For a quadratic equation :

y = a x ^ 2 + b x + c

the vertex ( x = h , y = k ) is found by computing :

x = h = – b / 2 a

and then evaluating y at h to find k.

In this case :

a = - 2

b = 4

h = - b / 2 a =

- 4 / [ 2 * ( - 2 ) ] =

- 4 / - 4

h = 1

The x - coordinate of the vertex :

x = 1

k = y = - 2 x ^ 2 + 4 x + 1

k = - 2 * 1 ^ 2 + 4 * 1 + 1

k = - 2 * 1 + 4 + 1

k = - 2 + 4 + 1

k = 3

y = 3

The y - coordinate of the vertex :

y = 3

The axis of symmetry is a vertical line through the vertex, so its equation is :

x = 3

( For all value of y , x = 1 )

Answer 2

Tipefeler:

The axis of symmetry is a vertical line through the vertex, so its equation is :

x = 1

( For all value of y , x = 1 )

Answer 3

or ... just complete the square

y = -2(x^2 -2x + ... ) + 1
= -2(x^2 - 2x + 1 - 1) + 1
= -2(x- 1)^2 + 3

all your requests can be read off that.

Answer 4

The drag force F (in pounds) of water on a swimmer can be modeled by F = 1.35s^2 where s is the swimmer’s speed ( in miles per hour). At what speed is the force minimized? **Note** ^ means "to the power of."