Flashcard 7 - Math Flashcard Set for the PERT

\(f(x)=ax^2+bx+c\)
Y-int: \((0,c)\)
X-int: set \(f(x)=0\) and solve for x by factoring (You can also use the quadratic formula.)
Axis of symmetry: \(x=\frac{-b}{2a}\)
Vertex: \((\frac{-b}{2a},f(\frac{-b}{2a}))\)

In the standard equation of a parabola shown as \(f(x) = ax^2 + bx + c\), a positive \(a\) indicates a parabola that opens upward with a vertical axis of symmetry given by the equation \(x=\frac{-b}{2a}\).

The y-intercept is found by solving for \(y\) when \(x = 0\). We do this as follows:

\[y = a\cdot0^2 + b\cdot0 + c\] \[y = c\]

Therefore, the parabola intercepts the y-axis at \((0, c)\).

The x-intercept is found by solving for \(x\) when \(y = 0\).

\(ax^2 + bx + c = 0\).

Solve for x by factoring or by using the quadratic formula.