Graphing Quadratic Functions in Standard Form

Every question gives you a quadratic function written in the standard form $y = ax^2 + bx + c$ together with its graph. Write down the five things asked for underneath each parabola. You can read them off the picture, or work them out from the formula and use the picture to check yourself - the marked points are the vertex and the y-intercept with the point opposite it.

Here is how to read the five answers straight out of $y = ax^2 + bx + c$:

The graph of every quadratic function is a parabola. The sign of a alone tells you which way it goes: $a > 0$ opens up, $a < 0$ opens down.
The vertex is the one point where the curve turns round. On a parabola that opens up it is the lowest point of the graph, so the vertex is a minimum; on one that opens down it is the highest point, so the vertex is a maximum.
The y-intercept is where the curve crosses the y-axis, so put $x = 0$: everything with an x in it disappears and only c is left. The point is $(0, c)$ - the constant at the end of the formula.
The axis of symmetry is the upright line the parabola folds onto itself along. It is $x = -\frac{b}{2a}$, and it always goes through the vertex.
So the vertex is found from that line: its x is $-\frac{b}{2a}$, and its y is what the formula gives you when you put that number back in.

An example. For $y = 2x^2 + 4x + 3$ we have $a = 2$, $b = 4$ and $c = 3$. Since $a > 0$ the parabola opens up and its vertex is a minimum. The y-intercept is $(0, 3)$. The axis of symmetry is $x = -\frac{4}{2 \cdot 2} = -1$, and $y = 2 \cdot (-1)^2 + 4 \cdot (-1) + 3 = 1$, so the vertex is $(-1, 1)$.

Reload the page and you get a new worksheet - all four functions are generated at random every time.