Question

suppose a parabola has a vertex in quadrant IV and a<0 in the equation y=ax^2+bx+c. how many real solutions will the equation ax^2+bx+c=0 have?

Answer 1

IV quadrant is below the x-axis .... which way is the parabola facing? up or down?

Answer 2

it depends on the values of b & c as well, but you can use the formula below for any quadratic:
\[b ^{2}-4ac > 0\] means there are 2 real roots
\[b ^{2}-4ac = 0\] means there is 1 repeated real root and
\[b ^{2}-4ac < 0\] means there are no real roots
this is becasue in the quadratic equation, the \[b ^{2}-4ac\] is the part in the square root, so determines whether the roots are real or not

Answer 3

Rethink your argument 08. If the vertex is in IV and the parabola opens down, you automatically know that the discriminant is negative because there are NO real solutions since the parabola does not cross the x axis;.

Answer 4

oh yeah, i didnt see the 'in quadrant IV' part

Answer 5

so no real roots?

Answer 6

Exactly

Answer 7

Does that look like it's going to cross the x axis?

Answer 8

cant it be like this?

Answer 9

No. The vertex is not in the fourth quadrant.