Higher November 2024 Paper 3 Q23
23 Sketch the graph of
\(y = x^2 - 6px - 7 \quad\) where \(\quad p \gt 0\)
showing the coordinates of the turning point, in terms of \(p\), and the coordinates of the intercept with the \(y\)-axis.
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| Sketch graph with minimum point at \((3p, -9p^2 - 7)\) in 4th quadrant and \(y\) intercept at \((0, -7)\) | B1 | for a curve drawn with intercept at the point \((0, -7)\) |
| M1 | for the start of a method to find the turning point, eg \((x - 3p)^2 \ldots\) or an \(x\) coordinate of \(3p\) at the vertex | |
| M1 | (dep) for a complete correct method to find the turning point, eg \((x - 3p)^2 - 9p^2 - 7\) or substitutes \(x = 3p\) into the equation to find \(y\) | |
| B1 | for turning point at \((3p, -9p^2 - 7)\) | |
| C1 | for a sketch of a parabola drawn with intercept at \((0, -7)\) and minimum turning point clearly shown as being at \((3p, -9p^2 - 7)\) in the 4th quadrant. |
Additional guidance
where … can be any constant term(s) but not term(s) in \(x\)
Allow \((3p)^2\) for \(9p^2\) throughout
A correct answer with no supportive working gets 0 marks