Question

? R(3,2) V(-3,4) S P T 2 X 0 1 y=f(x) y=g(x) ne sketch shows the graph of a function f, which is a straight line defined by y = mx + k such at the point V lies on the line, and the graph of a function g, which is a parabola with vertex R. ne straight line and parabola intersect at P and Q. The points S and T lie on the parabola and raight line, respectively, between P and Q. The line ST is parallel to the y-axis. 2.1 Calculate m and k, and hence write down the equation for f. 2.2 Find the equation of the parabola. 2.3 Find the maximum length of ST. At what value of z will ST be at its longest? (3) (4) (5) 2.4 What is the equation of the circle with centre P and radius equal to the distance from P to the origin? 2.5 What is the equation of the hyperbola through the point V? 2.6 Use the graphs to solve the inequality (f \cdot g)(x) \ge 0. (4) (1) (3)

          ?
R(3,2)
V(-3,4)
S
P
T
2
X
0
1
y=f(x)
y=g(x)
ne sketch shows the graph of a function f, which is a straight line defined by y = mx + k such
at the point V lies on the line, and the graph of a function g, which is a parabola with vertex R.
ne straight line and parabola intersect at P and Q. The points S and T lie on the parabola and
raight line, respectively, between P and Q. The line ST is parallel to the y-axis.
2.1 Calculate m and k, and hence write down the equation for f.
2.2 Find the equation of the parabola.
2.3 Find the maximum length of ST. At what value of z will ST be at its longest?
(3)
(4)
(5)
2.4 What is the equation of the circle with centre P and radius equal to the distance from P to the
origin?
2.5 What is the equation of the hyperbola through the point V?
2.6 Use the graphs to solve the inequality (f \cdot g)(x) \ge 0.
(4)
(1)
(3)

?
R(3,2)
V(-3,4)
S
P
T
2
X
0
1
y=f(x)
y=g(x)
ne sketch shows the graph of a function f, which is a straight line defined by y = mx + k such
at the point V lies on the line, and the graph of a function g, which is a parabola with vertex R.
ne straight line and parabola intersect at P and Q. The points S and T lie on the parabola and
raight line, respectively, between P and Q. The line ST is parallel to the y-axis.
2.1 Calculate m and k, and hence write down the equation for f.
2.2 Find the equation of the parabola.
2.3 Find the maximum length of ST. At what value of z will ST be at its longest?
(3)
(4)
(5)
2.4 What is the equation of the circle with centre P and radius equal to the distance from P to the
origin?
2.5 What is the equation of the hyperbola through the point V?
2.6 Use the graphs to solve the inequality (f ·g)(x) ≥0.
(4)
(1)
(3)

Added by Esther P.

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