Chapter 7.4, Problem 1PE

To determine

Fill in the blanks.

1. The graph of a quadratic equation $f\left(x\right)=a{x}^2+bx+c$ is a ______.
2. 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 $a\_\_\_\_\_\_0$ .
3. 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.
4. 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 minimum value of the function.
5. 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 ______.