Quadratic functions help?

Question

for the graph of the equation y=ax^2 what is the effect of a value of: 

a) a=1/4 

b) a= -3 

for the graph of the equation y=x^2+c what is the effect of a value of: 

a) c>0 

b) c<0

Answer 1

For the graph of y = x² + c

The quadratic equation represents a parabola in the graph.

y = ax² + bx + c

a = 1, b = 0, c = c

a) For c > 0

b² - 4ac = 0 - 4(1)(c)

= - 4c < 0

Discriminant b² - 4ac is negative means the equation has two imaginary roots.

There is no x intercepts.

If c > 0, the graph of parabola never touches the x - axis.

b) For c < 0

b² - 4ac = 0 - 4(1)( - c)

= 4c > 0

Discriminant b² - 4ac is positive means the equation has two distinct real roots.

There is two x intercepts.

If c < 0, the graph of parabola touches the x - axis at two points.

Answer 2

For the graph of y = ax²

The quadratic equation represents a parabola in the graph.

in this case the parabola vertex at origin.

a) For a = 1/4

The sign of a is positive, then the parabola opens upward.

b) For a = -3

The sign of a is negative, then the parabola opens downward.