Question

Which graph represents the function f(x) = -x^2 + 5

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we have the quadratic function

$f(x)=-x^{2}+5$

This is a vertical parabola open downward

The vertex is a maximum

Remember that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

In this problem

a=-1

(h,k)=(0,5) ----> vertex

The y-intercept is the point (0,5) ---> value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points $(\sqrt{5},0),(-\sqrt{5},0)$ --->values of x when the value of y is equal to zero  

using a graphing tool

The graph in the attached figure

Answer 2

The graph which represents the function is as in the attached image.

Quadratic function

The graph of the function can be predicted by determining the y-intercept, and x intercepts of the graph as follows;

• The y-intercept of the function is at; x = 0.

f(0) = -(0)² +5

• Therefore, the y-intercept is; (0, 5)

The x-intercept is at points;

• x = √5

• x= ±2.236

Read more on quadratic functions;

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