Functions

The function f(x)=−x²+4 is a downward‑opening parabola whose vertex occurs at x=0, giving a maximum value f(0)=4, so the output can be any number less than or equal to 4, i.e., y≤4. Choice A (y≥4) flips the inequality, assuming the parabola opens upward; that would be true for +x²+4, not the given function.

Plugging x = 2 into f(x) = 2x² − 3x + 1 gives f(2) = 2·4 − 3·2 + 1 = 8 − 6 + 1 = 3, so answer A is correct. Answer B (7) results from mis‑adding the terms (8 − 6 = 2, then adding 1 incorrectly as 5) or forgetting the subtraction sign, which inflates the value.

Plugging x = 2 into f(x) = 2x² − 3x + 1 gives f(2) = 2·4 − 3·2 + 1 = 8 − 6 + 1 = 3, so answer A is correct. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Choice A (y≥4) flips the inequality, assuming the parabola opens upward; that would be true for +x²+4, not the given function.
• !Choice A confuses the intercept with the slope, which is 3, not the coordinate where the line meets the axis.

Answer each from memory — you'll see instantly whether you're right and why.

Run a focused 10-question mini-mock on Functions and see it stick.