Chapter 11.4, Problem 1PE

a. The graph of a quadratic function, $f\left(x\right)=a{x}^2+bx+c=0$, is a ___________.

b. The parabola defined by $f\left(x\right)=a{x}^2+bx+c\left(a\ne 0\right)$ will open upward if a ________ 0 and will open downward if a ____________ 0.

c. If a parabola opens upward, the vertex is the (highest/lowest) point on the graph. If a parabola opens downward, the vertex is the (highest/lowest) point on the graph.

d. Given $f\left(x\right)=a{\left(x-h\right)}^2+k\left(a\ne 0\right)$, the vertex of the parabola is given by the ordered pair____________. If the parabola opens____________, the value of k is the minimum value of the function. If the parabola opens _____________, the value of k is the maximum value of the function.

e. Given $f\left(x\right)=a{\left(x-h\right)}^2+k\left(a\ne 0\right)$, the axis of symmetry of the parabola is the vertical line that passes through the _______________. An equation of the axis of symmetry is _________________.