A few exercises - Problems
Lessons on Quadratics: [Summary
- the Program] [ Graphing Exercises ] [ Graph y = a[(x-h)^2 +k] ] [ Factoring Quadratics ] [ Difference of Two Squares ] [ Completing the Square ] [ Convert to Standard Form (Arith) ] [ Quadratic Formula ] [ Finding Coefficients ] [ Applications ] [ Quadratics Summary ] [ Exercises ] [ Quadratics Overview Page ]
1. (6 points) (i) Use the quadratic
formula to solve x2-3x-4= 0.
(4 points) (ii) Find the
value of y on the axis of symmetry of the quadratic y = x2-3x-4.
(4 points) (iii) Use the
results of (i) and (ii) to sketch the curve y = x2-3x-4.
2. (4 points) Find the intersection points of the
quadratic y = x2 and the line y = 3x+4.
3. (6 points) (i) Sketch the curve pq = 1 in
the first quadrant of the pq plane.
(4 points) (ii) Give the definition
of ln(x) for x > 1.
(4 points) (iii) Shade in the area
under this curve pq = 1 that gives or defines ln(4).
4. (8 points) (Step I) Complete the square
for x2-6x-8 and simplify the result.
(6 points) (Step II) Use the result
of step I and the difference of two squares to factor x2-6x-8
(4 points) (Step III) Use the
result of step II to solve x2-6x-8 = 0
5. (3 points) (i) Solve x2-5x+ 4 =0 using
factorization by inspection. Show all ways for 4 to equal the product AB
of two integers A and B.
(3 points) (ii) Solve x2-5x+4 =
0 with the quadratic formula. Show work.
(4 points) (iii) Solve x2 - 5x
+ 4 =0 starting with the method of completing the square. Show work.
6. (4 points) (i) Find the x- and y-intercepts
of the quadratic y = x2-5x+4 and the straight line y
= -2x + 8 with the x- and y-axes. Hint: See 5(ii) or (iii).
(3 points) (ii) Sketch the curves y
= x2-5x+4 and y = -2x + 8. Identify the axis of symmetry
for the quadratic. Label axes and all intercepts.
(3 points) (iii) Find the coordinates of the
intersection points for the quadratic y = x2-5x+4
and line y = -2x + 8. Show reasoning. Hint: x2-3x-4
= (x-4)(x+1).
7. (3 points) (i) Solve x2-5x+ 4 =0 using
factorization by inspection. Show all ways for 4 to equal the product AB
of two integers A and B.
(3 points) (ii) Solve x2-5x+4 =
0 with the quadratic formula. Show work.
(4 points) (iii) Solve x2 - 5x
+ 4 =0 starting with the method of completing the square. Show work.
8. (4 points) (i) Find the x- and y-intercepts
of the quadratic y = x2-5x+4 and the straight line y
= -2x + 8 with the x- and y-axes. Hint: See 7(ii) or (iii).
(3 points) (ii) Sketch the curves y
= x2-5x+4 and y = -2x + 8. Identify the axis of symmetry
for the quadratic. Label axes and all intercepts.
(3 points) (iii) Find the coordinates of the
intersection points for the quadratic y = x2-5x+4
and line y = -2x + 8. Show reasoning. Hint: x2-3x-4
= (x-4)(x+1).