Today we had a quick quiz on factoring, but we also reviewed at least 2 graphing problems and started the discovery worksheet on sums and products Download Making Connections about Roots . Please be aware that, if you got this worksheet in class, G(x) = 6x2 - x - 1 (a typo) and q(x) really can't be factored over the reals, but it still has roots (remember the quadratic formula!). Also, realize that even if you can't complete the proof on the back (and you really should be able to do that with the hints given!), you can still work the problems at the end of the worksheet.
Here are answers to the Acc. Math II Worksheet #2 on Characteristics of Quadratics in Various Forns.
1) Vertex: (3/2, 9) (Easy to find thanks to vertex form)
Axis of symmetry: x = 3/2 (Easy to find knowing the vertex)
Opens DOWN because the leading coeficient is negative.
Maximum value is 9 because that's the y-value of the vertex.
X-intercepts are 0, -3, but we needed to factor the standard form to get that.
Standard form: y = -4x2+ 12x (because the x terms cancelled.
Intercept (or factored) form: y = -4x(x - 3)
2. Vertex (-3, -6) (I averaged the x-intercepts.
Axis of symmetry: x = -3 It opens up and the minimum value of -6.
The intercepts are -9 and 3 which can be found easily by setting the factors equal to 0 and solving for x.
Standard form is (1/6)x2 + x - 9/2 and vertex form is (1/6)(x + 3)2 - 6
3. Vertex (-1, 18) Axis of symmetry is x = -1 It opens up and has a minimum value of -18. The x-intercepts are -4 and 2. In intercept form it is f(x) = 2(x + 4)(x - 2) and in vertex form it is y = 2(x + 1)2 - 18
4. The vertex is (5/3, -16/3) and the axis of symmetry is x = 5/3. It opens up and has a minimum value of -16/3. The x-intercepts are at 1/2 and 3. Written in standard form, it looks like y = 3x2 - 10x + 3, and written in vertex form, it looks like: 3(x - 5/3)2 - 16/3
5. The vertex is (-2, -4/5) and the axis of symmetry is x = -2. It opens down and attains a minimum value of -4/5. There are no x-intercepts, so there is no intercept form. (There is a factored form, however! It is y = -2(x +2 + i(sqrt(10))/5)(x + 2 - i(sqrt(10))/5).) The standard form is y = -2x2 - 8x - 44/5.
And Selected answers to the back of the "Making Connections..." worksheet are:
f(x) = a(x - r)(x - s) = ax2 - a(r + s)x + ars
The coefficient of x2 is a = a, the coefficient of x is b = -a(r + s) and the constant term is c = ars.
-b/a = -(-a(r + s))/a = a(r + s)/a = r + s
You can do the rest!
