A quadratic function has roots (2, 0) and (-7, 0). Which of the following could represent the quadratic function?

1. y = x² − 9x + 14
2. y = x² + 9x + 14
3. y = x² − 5x + 14
4. y = x² + 5x − 14

A
Incorrect. Did you use (x − 2) and (x + 7) as your factors?

B
Incorrect. Did you use (x − 2) and (x + 7) as your factors?

C
Incorrect. Did you use (x − 2) and (x + 7) as your factors?

D
Correct! The factors (x − 2)(x + 7) can be multiplied to form x² + 5x − 14.

Which of these functions does not have roots (1,0) and (6,0)?

1. y = x² − 7x + 6
2. y = 2x² − 14x + 12
3. y = -3x² + 21x − 18
4. y = x² + 7x + 6

A
Incorrect. This factors into y = (x − 1)(x − 6).

B
Incorrect. This factors into y = 2(x − 1)(x − 6).

C
Incorrect. This factors into y = -3(x − 1)(x − 6).

D
Correct! This factors into y = (x + 6)(x + 1), which has roots at (-6,0) and (-1,0).

Which of the statements below about quadratic functions and their roots, real or complex, are correct?

1. A quadratic function with real roots will always have two distinct and different roots.
2. A quadratic function with complex roots will always have complex roots that are conjugates of each other.
3. Real roots for quadratic functions can be double roots.
4. A quadratic function can have both real and complex roots.

A. I and II only
Incorrect. Recall that quadratic functions have two real roots or even one double root.

B. II and III only
Correct!

C. I and IV only
Incorrect. Quadratic functions can only have a maximum of two roots, but cannot have both real and complex roots.

D. I, II, III and IV
Incorrect. Quadratic functions can have two real roots, a real double root, or complex roots.

A quadratic function has real roots at x = -4 and x = 5. Which quadratic equation below, when solved, could be represented by these roots?

A. -20 = x² + 9x
Incorrect. Go back and check the factors that correlate to the roots mentioned in the problem.

B. -x² + x = 20
Correct!

C. x² + x = 20
Incorrect. Check your signs as you solved the quadratic equation for the roots.

D. -20 = x² − 9x
Incorrect. Go back and check the factors that correlate to the roots mentioned in the problem.

Raul is trying to write a quadratic function in standard form. He knows that the quadratic function has a complex root at x = 2 – i. After multiplying, he writes the quadratic function as f(x) = x² + 3. What is incorrect about this quadratic function that Raul has written?

A. The function should have a value of +4x for the coefficient, b.
Incorrect. The coefficient on the x-term is correct as -4.

B. The function should have a value of 4 for the constant, c.
Incorrect. As a hint, remember that i² has a value of -1.

C. The function should have a value of 5 for the constant, c.
Correct!

D. There is nothing incorrect. Raul did not make any mistakes.
Incorrect. Raul did make a mistake in his multiplication.