Question

q2 - m25 - hwk 6 - quadratic/vertex form review w/ desmos due: december 14 at 11:59 pm grade: 25% problem: vertex form coefficients compare features of tables vs. graphs evaluate quadratic functions scientific calculator graphing calculator has a answer attempt 1 out of 2 the value of f(x) is and there is no value. the value of g(x) is and there is no value than g(x). therefore f(x) x | -5 | -4 | -3 | -2 | -1 g(x) | -3 | 0 | 1 | 0 | -3

Explanation:

Step1: Analyze the table for \( g(x) \)

The table for \( g(x) \) has values: when \( x = -5 \), \( g(-5) = -3 \); \( x = -4 \), \( g(-4) = 0 \); \( x = -3 \), \( g(-3) = 1 \); \( x = -2 \), \( g(-2) = 0 \); \( x = -1 \), \( g(-1) = -3 \). This is a quadratic - like (symmetric) function. The maximum value of \( g(x) \) occurs at \( x=-3 \) with \( g(-3) = 1 \).

Step2: Determine the nature of \( f(x) \) (assuming \( f(x) \) is a quadratic function, maybe from context)

Since the problem is about comparing features of tables (for \( g(x) \)) and probably a graph (for \( f(x) \)) of quadratic functions. If we assume \( f(x) \) has a maximum or minimum. But from the table of \( g(x) \), the maximum value of \( g(x) \) is \( 1 \). If \( f(x) \) has a maximum value greater than \( 1 \) (or minimum, but the context of "value of \( f(x) \) is... and there is no... value" suggests maximum or minimum). Wait, the table of \( g(x) \) is symmetric around \( x = - 3 \), so it's a parabola opening downwards (since the values increase to \( x=-3 \) then decrease). So the maximum value of \( g(x) \) is \( 1 \). If \( f(x) \) has a maximum value (assuming it's a downward - opening parabola) greater than \( 1 \), or a minimum value (if upward - opening) less than the minimum of \( g(x) \). But from the given structure, let's assume we are comparing maximum values. The maximum of \( g(x) \) is \( 1 \). If \( f(x) \) has a maximum value (say, if \( f(x) \) is a quadratic with vertex giving a higher maximum), but since the problem is incomplete in the image, but from the table of \( g(x) \), the maximum value of \( g(x) \) is \( 1 \).

Wait, the original problem seems to be about comparing the maximum (or minimum) of \( f(x) \) and \( g(x) \). From the table of \( g(x) \), the function \( g(x) \) is symmetric about \( x=-3 \), and the maximum value of \( g(x) \) is \( 1 \) (at \( x = - 3 \)). If we assume that \( f(x) \) has a maximum value (for example, if \( f(x) \) is a quadratic function with a higher maximum), but since the user's image has some missing parts, but based on the table of \( g(x) \), the maximum value of \( g(x) \) is \( 1 \).

Answer:

(Assuming we are finding the maximum of \( g(x) \)) The maximum value of \( g(x) \) is \( 1 \). (If we assume \( f(x) \) has a maximum greater than \( 1 \), but with the given table, the key value from \( g(x) \)'s table is \( 1 \) as its maximum)