1. ## intercepts of graph

without graphing deteermine the number of x intercepts of the graph of y=4x^2-9x+4

for waht values of b does the quadratic function y=x^2+bx+7 have no x intercepts?

for what values does the quadratic function y=x^2-6x+k have two x intercepts?

for what value of k does the quardatic function y=-3x^2-bx+12 have exatcly one x intercept?

2. Originally Posted by gumi
without graphing deteermine the number of x intercepts of the graph of y=4x^2-9x+4

for waht values of b does the quadratic function y=x^2+bx+7 have no x intercepts?

for what values does the quadratic function y=x^2-6x+k have two x intercepts?

for what value of k does the quardatic function y=-3x^2-bx+12 have exatcly one x intercept?
1 quadratic formula $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ using the setup $\displaystyle ax^2+bx+c=0$

2 when the discrminant $\displaystyle \sqrt{b^2-4ac}$ in the quadratic formula is negative

3. two solutions when $\displaystyle \sqrt{b^2-4ac}$ is positive

4. one solutiong when $\displaystyle \sqrt{b^2-4ac}$ is equal to 0

3. You can tell a lot about a quadratic by looking at its discriminant

$\displaystyle b^{2}-4ac$.

If the discriminant is positive, then it has two real and unequal roots.

If it is 0, then it has one root of mutiplicity 2.

If it is negative, then it has no real roots.

For the second one, $\displaystyle x^{2}+bx+7=0$

If it does not cross the x-axis, then it has no real roots and the discrimiant must be negative.

$\displaystyle b^{2}-4(1)(7)<0$

$\displaystyle b^{2}-28<0$

$\displaystyle b^{2}<28$

$\displaystyle b<\sqrt{28}$

See?. Try it with the other problems.