Respuesta :
A parabola is the graph of a quadratic function,
that is the graph of [tex]f(x)=a x^{2} +bx+c[/tex], where a is not 0.
from a, b and c we can derive the following informations about the shape of a parabola:
if a>0, the parabola opens upwards.
if a<0, the parabola opens downwards.
Consider the discriminant [tex]D= b^{2} -4ac[/tex]
If D>0, the parabola intersects the x-axis at 2 points.
If D=0, the parabola intersects the x-axis at 1 point.
If D<0, the parabola does not intersect the x axis.
"the vertex of a parabola is in the first quadrant and the parabola opens upwards."
the vertex is in the first quadrant means that the vertex is above the x-axis, and it opens upwards, so the parabola does not intersect the x-axis.
This means that:
Answer: a>0, the discriminant D<0
that is the graph of [tex]f(x)=a x^{2} +bx+c[/tex], where a is not 0.
from a, b and c we can derive the following informations about the shape of a parabola:
if a>0, the parabola opens upwards.
if a<0, the parabola opens downwards.
Consider the discriminant [tex]D= b^{2} -4ac[/tex]
If D>0, the parabola intersects the x-axis at 2 points.
If D=0, the parabola intersects the x-axis at 1 point.
If D<0, the parabola does not intersect the x axis.
"the vertex of a parabola is in the first quadrant and the parabola opens upwards."
the vertex is in the first quadrant means that the vertex is above the x-axis, and it opens upwards, so the parabola does not intersect the x-axis.
This means that:
Answer: a>0, the discriminant D<0
