Question

learning check
given the equation or graph, classify the function type
$y = -3x^2 + 5$
$y = 5^x$
$y = \sqrt3{x} + 2$

Explanation:

1. For $y=-3x^2+5$, it follows the form $y=ax^2+bx+c$ (here $b=0$), which is the standard quadratic function structure.
2. For $y=5^x$, it has a constant base raised to a variable exponent, defining an exponential function.
3. The provided graph shows a curve with the shape of a cubic function (S-shaped, with one local maximum and one local minimum, matching the end behavior of cubic polynomials).
4. For $y=\sqrt[3]{x+2}$, it is a cube root function, a type of radical function with a 3rd root.

Answer:

1. $y=-3x^2+5$: Quadratic function
2. $y=5^x$: Exponential function
3. Provided graph: Cubic function
4. $y=\sqrt[3]{x+2}$: Cube root (radical) function