Quadratics

Question 1

. Sketch the following graphs showing all intercepts with the coordinate axes and the turning point.
a. y = (x + 1)(x − 3)
b. y = (x − 5)(2x + 1)
d. y = (1 − 3x)(4 + x)

Answer 1

a. y = (x + 1)(x − 3)
The y-intercept is (0, −3).
The x-intercepts are (−1, 0) and (3, 0)
The turning point is (1, −4).

b.y int= (0, -5)
x ints are -0.5 and 5
TP=(9/4, 121/8)

d. y int is 4
x ints are -4, 1/3
TP= (-11/3, 169/12)

Question 2

a. State the two linear factors of the equation of the
parabola whose x-intercepts occur at x = 3 and at x = 8 and from a possible equation for this
parabola.

b. The x-intercepts of a parabola occur at x = −11 and x = 2. From a possible equation for this parabola.

Answer 2

a For an x-intercept at x = 3, x − 3 would be a factor of the
equation.
For an x-intercept at x = 8, x − 8 would be a factor of the
equation.
A possible equation is y = (x − 3)(x − 8) but any answer in
the form y = a(x − 3)(x − 8) would be correct.

b For an x-intercept at x = −11, x + 11 would be a factor of
the equation.
For an x-intercept at x = 2, x − 2 would be a factor of the
equation.
A possible equation is y = (x + 11)(x − 2) but any answer
in the form y = a(x + 11)(x − 2) would be correct.