Answer: 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)
<u>Step-by-step explanation:</u>
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
3) 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
x = 1 x = 3 --> zeros are 1 and 3