Question

can someone help me with this one...
Compare and contrast the two quadratic equations below. describe the following:

The direction each parabola opens
The vertex of each parabola
y = x2 − 2x
y = −2x2 + 4x − 3

Answer 1

the general form is

f(x) = ax^2 + bx + c

the 1st equation

concave up, since a>0

f(x) = x(x - 2)

has x intercepts at x = 0 and x = 2

the line of symmetry is x = 1

y intercept of y = 0

and a minimum value of y = -1

the 2nd equation

concave down since a<0

is negative definate since the discriminant

\[\Delta = 4^2 - 4\times(-2)\times(-3) = -10\]

which means the curve doesn't cut the x - axis

has a line of symmetry of x = 1

has a maximum value of y = -1

y intercept at y = -3

hope this helps

Answer 2

sure thanks <3