Mathematics: Consider the polynomial function y=2(x−2)^3+5 when investigating and analyzing. domain [ Choose ] range [ Choose ] zero [ Choose ] x-intercept [ Choose ] y-intercept [ Choose ] continuity [ Choose ] increase [ Choose ] decrease [ Choose ] maximum [ Choose ] minimum [ Choose ] if x = 6 [ Choose ] as x → -∞ [ Choose ] as x → +∞ [ Choose ] vertical asymptote [ Choose ] horizontal asymptote [ Choose ]

Consider the polynomial function y=2(x−2)^3+5 when

jenna34032

19.08.2021

The minimum is -5

The range is $y \ge -5$

f(14) = 2739

Step-by-step explanation:

Given

y = 14x^2 - 5

Solving (a): The minimum

A quadratic function is represented as:

y = ax^2 + bx + c

If a > 0, then the function has a minimum

By comparison

a = 14 --- the function has a minimum

b = 0

c = -5

To calculate the minimum, we first calculate the following is calculated as:

$m = -\frac{b}{2a}$

So, we have:

$m = -\frac{0}{2*14}$

m = 0

So, the minimum is at f(m)

We have: y = 14x^2 - 5

f(0) = 14 *0^2 - 5

f(0) = - 5

Solving (b): The range

In (a), we have:

f(0) = - 5 --- the minimum

This implies that the smallest value of y on the graph is -5.

So, the range is:

$r = \{y|y\ge -5\}$

Solving (c): f(14)

We have:

y = 14x^2 - 5

So:

f(14) = 14 * 14^2 - 5

f(14) = 2739

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