SOLUTION: the parabola which is the graph of the function f: y= ax^2+bx+c, b>0,c<0 does not have any common point with the x-axis the top of this parabola lies in the same quadrant as the po

Question 436189: the parabola which is the graph of the function f: y= ax^2+bx+c, b>0,c<0 does not have any common point with the x-axis the top of this parabola lies in the same quadrant as the point with the coordinates A. {-1,-1} B.{-3,2} C.{2,-2} D. {1,1} AND PROVE THE ANSWER
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Since , then , so the entire parabola must be contained within the third and fourth quadrants. Hence, .

The vertex of the parabola occurs at . Since b is positive and a is negative, will be positive. The vertex has a positive x-coordinate and a negative y-coordinate, so it lies in the fourth quadrant, and choice C is correct.
RELATED QUESTIONS
The graph of y=ax^2 + bx + c is a parabola with vertical axis of symmetry. The vertex of... (answered by solver91311)

Which statement must be true if a parabola represented by the equation y = ax^2 + bx + c... (answered by drk,Alan3354,JimboP1977)

I have a graph that has an x-axis of (0.67, 0), an x-axis of (-1, 0) and a y-axis of (0,... (answered by stanbon)

Please help with the following: 1. Is the graph of f(x) = x^1171−5x^109 +3... (answered by richard1234)

How do you find real numbers a,b and c so that the graph of the function {{{ y=ax^2+bx+c... (answered by josgarithmetic,MathTherapy)

Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), a... (answered by josgarithmetic)

The graph of a certain quadratic y = ax^2 + bx + c is a parabola with vertex (-4,0) which (answered by MathLover1,ikleyn,MathTherapy)

The graph of y=ax^2+bx+c intersects the x-axis at two points. Which statement is true... (answered by jim_thompson5910)

Let C be the plane curve y=f(x) defined by the cubic function f(x)= x^3 - 4x^2 + ax + b... (answered by robertb)