Question

If the graph of quadratic polynomial intersect the x axis at two points ,then the shape of the parabola is

Answer 1

1) If the required graph , intersects the x-axis at two distinct points,then shape of parabola will be look like as shown in figure.

Let us take example of

$f(x)=(x-2)(x-10)\\ \\=x^2-12x+20$

Here, Two points are x=2 and x=10.

In this case , Discriminant of the quadratic equation is not equal to zero and greater than 0.

Similarly, a graph can be drawn with parabola opening downward where coefficient of x^2 is greater than 0.

Appropriate example will be :

$f_1(x)=_(x-2)(x-10)\\ \\=-x^2+12x-20$

Here,too points intersecting the x-axis remains same but shape goes parabola opening downward.

Answer 2

Answer:

open upward as it intersect at two points