Sketching Quadratics
Sketching Quadratics
For each of these, sketch a graph marking clearly any points where it
crosses the axes.
For each of these, sketch a graph marking clearly any points where it
crosses the axes.
1. y = (x − 4)(x − 1)
11. y = x2 + 2x + 1
1. y = (x − 4)(x − 1)
11. y = x2 + 2x + 1
2. y = (x − 2)(x − 1)
12. y = x2 − 2x + 1
2. y = (x − 2)(x − 1)
12. y = x2 − 2x + 1
3. x(x − 2)
13. y = x2 + 5x + 4
3. x(x − 2)
13. y = x2 + 5x + 4
4. y = (x + 1)(x − 1)
14. y = x2 + 7x + 12
4. y = (x + 1)(x − 1)
14. y = x2 + 7x + 12
5. x(x − 5)
15. y = x2 − 3x − 10
5. x(x − 5)
15. y = x2 − 3x − 10
6. y = (x − 10)(x + 2)
16. y = x2 + 3x − 10
6. y = (x − 10)(x + 2)
16. y = x2 + 3x − 10
7. y = (−x + 10)(x + 2)
17. y = x2 + 5x − 14
7. y = (−x + 10)(x + 2)
17. y = x2 + 5x − 14
8. y = (x + 3)(x − 4)
18. y = x2 − 7x − 30
8. y = (x + 3)(x − 4)
18. y = x2 − 7x − 30
9. y = (x − 3)(x − 2)
19. y = x2 − 17x − 30
9. y = (x − 3)(x − 2)
19. y = x2 − 17x − 30
10. y = (x + 15)(x − 4)
20. y = x2 − 6x − 8
10. y = (x + 15)(x − 4)
20. y = x2 − 6x − 8
Don’t forget that a line crosses the y-axis when x = 0 and crosses the
x-axis when y = 0.
Don’t forget that a line crosses the y-axis when x = 0 and crosses the
x-axis when y = 0.
If x = 0 then put a zero in where there is an x and then find out what y
equals.
If x = 0 then put a zero in where there is an x and then find out what y
equals.
If y = 0 then put a zero in where there is a y and rearrange the equation
to find out what y equals.
If y = 0 then put a zero in where there is a y and rearrange the equation
to find out what y equals.
For example, to find out where y = (x + 7)(x + 2) crosses the y-axis, put
in 0 instead of x and get y = (0 + 7)(0 + 2) = 7 × 2 = 14. To find where
it crosses the x-axis, put in 0 instead of y and get (x + 7)(x + 2) = 0. If
two things multiplied make zero, then at least one of them must be zero,
so either x + 7 = 0 ⇒ x = −7 or x + 2 = 0 ⇒ x = −2.
For example, to find out where y = (x + 7)(x + 2) crosses the y-axis, put
in 0 instead of x and get y = (0 + 7)(0 + 2) = 7 × 2 = 14. To find where
it crosses the x-axis, put in 0 instead of y and get (x + 7)(x + 2) = 0. If
two things multiplied make zero, then at least one of them must be zero,
so either x + 7 = 0 ⇒ x = −7 or x + 2 = 0 ⇒ x = −2.
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Sketching Quadratics
Sketching Quadratics
For each of these, sketch a graph marking clearly any points where it
crosses the axes.
For each of these, sketch a graph marking clearly any points where it
crosses the axes.
1. y = 3x2 + 4x + 1
6. y = 4x2 − 31x + 21
1. y = 3x2 + 4x + 1
6. y = 4x2 − 31x + 21
2. y = 2x2 + 7x + 6
7. y = −2x2 − 7x + 4
2. y = 2x2 + 7x + 6
7. y = −2x2 − 7x + 4
3. y = 2x2 − 5x − 3
8. y = 14x2 − 3x − 2
3. y = 2x2 − 5x − 3
8. y = 14x2 − 3x − 2
4. y = 6x2 − x − 2
9. y = −12x2 − x + 1
4. y = 6x2 − x − 2
9. y = −12x2 − x + 1
5. y = 2x2 − x − 15
10. y = 4x2 − 1
5. y = 2x2 − x − 15
10. y = 4x2 − 1
Don’t forget that a line crosses the y-axis when x = 0 and crosses the
x-axis when y = 0.
Don’t forget that a line crosses the y-axis when x = 0 and crosses the
x-axis when y = 0.
If x = 0 then put a zero in where there is an x and then find out what y
equals.
If x = 0 then put a zero in where there is an x and then find out what y
equals.
If y = 0 then put a zero in where there is a y and rearrange the equation
to find out what y equals.
If y = 0 then put a zero in where there is a y and rearrange the equation
to find out what y equals.
For example, to find out where y = (x + 7)(x + 2) crosses the y-axis, put
in 0 instead of x and get y = (0 + 7)(0 + 2) = 7 × 2 = 14. To find where
it crosses the x-axis, put in 0 instead of y and get (x + 7)(x + 2) = 0. If
two things multiplied make zero, then at least one of them must be zero,
so either x + 7 = 0 ⇒ x = −7 or x + 2 = 0 ⇒ x = −2.
For example, to find out where y = (x + 7)(x + 2) crosses the y-axis, put
in 0 instead of x and get y = (0 + 7)(0 + 2) = 7 × 2 = 14. To find where
it crosses the x-axis, put in 0 instead of y and get (x + 7)(x + 2) = 0. If
two things multiplied make zero, then at least one of them must be zero,
so either x + 7 = 0 ⇒ x = −7 or x + 2 = 0 ⇒ x = −2.
2x2 − x − 6
Look for
of !12
factors
!6)
e
im
(2 t s
2x2 − x − 6
Look for
of !12
factors
!6)
e
im
(2 t s
2x2 − 4x + 3x − 6
2x2 − 4x + 3x − 6
2x(x − 2) + 3(x − 2)
2x(x − 2) + 3(x − 2)
(2x + 3)(x − 2)
(2x + 3)(x − 2)
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