Let f(x) be a quadratic function and c

Zane Decker

Zane Decker

Answered question

2022-04-16

Let f(x) be a quadratic function and c constant. Which of the following statements is correct?
a) There is a unique value of c such that y = f(x) - c has a double root.
b) There is unique value of c such that y = f(x-c) has a double root.

Answer & Explanation

Jax Burns

Jax Burns

Beginner2022-04-17Added 13 answers

Step 1
y=f(x)c
moves the parabola up or down. There is only one value of c that will put the vertex of the parabola coincident with the x-axis.
y=f(xc)
moves the parabola left or right. No matter what the value of c is, the number of roots will not change.
prangijahnot

prangijahnot

Beginner2022-04-18Added 17 answers

Step 1
(a) is correct but (b) is incorrect. If f(x) has no real roots, then f(xc) has no real roots either for any c. For part (a), you can just subtract the value of f at the vertex.

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