\(y = x^2 - 6px - 7 \quad\) 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)
Mark scheme
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
