Property 1
Parabola
The graph of a quadratic function is called a parabola.
\(f(x)=ax^2+bx+c\)
if \(a>0\), the arms of the parabola are upwards.
if \(a<0\), the arms are downwards.
If the absolute value of \(a\) increases the parabola shrinks towards the vertical axis.
Finding Quadratic Equations with Known Roots
\(f(x)=a(x-x_1)(x-x_2)\)
\(f(0)=c=a\cdot x_1x_2\)
The factor \(a\) is found from this equation.
Parabolas Related to Δ's Condition
\(\Delta=b^2-4ac\)
\(\Delta>0\): two different real roots; the parabola cuts the x-axis at two points.
\(\Delta=0\): equal roots; the parabola is tangent to the x-axis.
\(\Delta<0\): no real root; the parabola does not cut the x-axis.
1.
\(f(x)=?\)
2.
\(f(x)=?\)
3.
\(f(x)=?\)
4.
\(f(x)=?\)
5.
\(f(x)=?\)
6.
\(f(x)=?\)
7.
\(f(x)=?\)
8.
\(f(x)=?\)
9.
\(f(x)=?\)