The graph shows the relation of the form y = mx2 2 + nx + r, where m, n and r are constants. Using the graph: (a) state the scale used on both axes; (b) fin...

The graph shows the relation of the form y = mx2 ${}^2$ + nx + r, where m, n and r are constants.

Using the graph:

(a) state the scale used on both axes; (b) find the values of m, n and r; (c) find the gradient of the line through P and Q; (d) state the range of values of x for which y > Q.

Answer Details

(a) x-axis: 2 cm to 2 units or 1 cm to 1 unit

y-axis: 2 cm to 10 units or 1 cm to 5 units

(b) x = -2, x = 4

(x+2)(x-4) = 0

x2 ${}^2$ -4x + 2x -8 = 0

x2 ${}^{\mathrm{<br>}}$ -2x - 8 = 0

y = 8 + 2x - x(curve has a max. point)

m = -1,n = 2, r =8

(c) P(-5,-27),Q(3,5)

Gradient = 5+273+5 $\frac{\mathrm{<br>}}{}$

= 328 $\frac{32}{8}$

= 4

 (d) Range: {x:-2 < x < 4)