Which of the following is the quadratic parent function?

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer:

A. F(x)=x^2

Step-by-step explanation:

Quadratic function is the function which has degree two

Degree is the highest power of a polynomial

In option B we have |x| in which degree is one hence, discarded

In option C we have in which degree is three hence, discarded

In option D we have x which is a linear function being of degree one. Hence, discarded.

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Answer:

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Here's the examples:

The horizontal line $y = 4$ intercepts the parabola twice: the system $y = x^2,\ y = 4$ is solved by $x^2=4 \implies x = \pm 2$
The horizontal line $y=0$ intercepts the parabola only once: the system is $y=x^2,\ y=0$ which yields $x^2=0\implies x=0$ which is a repeated solution
The horizontal line $y=-5$ intercepts the parabola only once: the system is $y=x^2,\ y=-5$ which yields $x^2=-5$ which is impossible, because a squared number can't be negative.