Answer:
10. Yes, if you know where the y-intercept is, and your zeros, the line is fixed, and you have a curve that is already fixed based on the y-intercept. However without the y-intercept, your zero's would be useless.
11. x=−1x or =−5/2 (x=−1 or x=−2.5)
which becomes
13. x<4 or x>4
Explanation:
(x - 4)^2 > 0
Take the square root of each side
±sqrt((x - 4)^2) >sqrt( 0)
x-4 > 0 or -(x-4)>0
Solving the first inequality
Add 4 to each side
x>4
Solving the second inequality
Divide each side by -1, remembering to flip the inequality
x-4 <0
Add 4 to each side
x < 4
14. 1) NO. the zeros are: 2 and -7
2) (x + 5)² has a middle term when in expanded form
3) Factoring provides the Intercept form: y = a(x - p)(x - q)
Explanation:
1) y = (x - 2)(x + 7)
To find the zeros, set the factors equal to zero:
0 = x - 2 0 = x + 7
x = 2 x = -7
The zeros are 2 and -7.
The student did not set the factors equal to zero.
2) (x + 5)² = (x + 5)(x + 5)
= x² + 5x + 5x + 25
= x² + 10x + 25 ≠ x² + 25
15. The Intercept form of a quadratic equation is: y = a(x - p)(x - q) where p and q are the x-intercepts. Notice that the intercept form IS the factored form. Set the factors equal to zero to find the x-intercepts.
y = x² - 4x + 3
y = (x - 1)(x - 3) --> Intercept form
0 = (x - 1)(x - 3) --> finding the zeros (aka x-intercepts)
0 = x - 1 0 = x - 3
16. The x-intercepts of the graph of the quadratic function is 1, 3.
Explanation:
Now for x-intercepts, y = 0.
⇒ x² - 4x + 3 = 0
Factoring we get,
⇒ x² - 3x - x + 3 = 0
⇒ x(x - 3) - 1(x - 1) = 0
⇒ (x - 1) (x - 3) = 0
Thus we get,
x = 1, 3
this is the required x-intercepts of the graph of the quadratic function.
Thus, the x-intercepts of the graph of the quadratic function is 1, 3.