Question

\cut the parabola in half\ miguel has a parabola where, \... the y - axis cuts the parabola in half.\ (1) use the sketch tool to show what his graph could have looked like. (2) what other word or phrase could we use for \cut the parabola in half\?

Explanation:

1. For part (1), since the \(y -\)axis cuts the parabola in half, the parabola is symmetric about the \(y -\)axis. A simple example of such a parabola is \(y=x^{2}\). When \(x = 2\), \(y=4\); when \(x=- 2\), \(y = 4\). We can sketch a parabola opening upwards (or downwards) with vertex at the origin (or other points on the \(y -\)axis) on the coordinate grid. For example, a parabola \(y=x^{2}\) has points \((-2,4)\), \((-1,1)\), \((0,0)\), \((1,1)\), \((2,4)\) etc.
2. For part (2), the technical term for a line that cuts a parabola (or a symmetric figure) in half (such that the two - halves are mirror images of each other) is the "axis of symmetry". A parabola \(y = ax^{2}+bx + c\) has the axis of symmetry given by the formula \(x=-\frac{b}{2a}\). When \(b = 0\) (the case when the \(y -\)axis is the axis of symmetry), \(x = 0\) (the \(y -\)axis).

Answer:

1. Sketch a parabola like \(y=x^{2}\) (opening upwards with vertex at \((0,0)\)) or \(y=-x^{2}\) (opening downwards with vertex at \((0,0)\)) or \(y=(x - 0)^{2}+k\) (vertex at \((0,k)\)) on the coordinate grid.
2. Axis of symmetry.