Maths-

General

Easy

Question

# Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . G(x)= -x^{2}+4x+5

Hint:

### For a quadratic function is in standard form, f(x)=ax2+bx+c.

A vertical line passing through the vertex is called the axis of symmetry for the parabola.

Axis of symmetry x=−b/2a

Vertex The vertex of the parabola is located at a pair of coordinates which we will call (*h, k*). where h is value of x in axis of symmetry formula and k is f(h).

The *y*-intercept is the point where a graph crosses the *y*-axis. In other words, it is the value of *y* when x=0.

## The correct answer is: ( 2 , 9 )

### This quadratic function is in standard form, f(x)=ax^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In g(x)= -x^{2}+4x+5, a= -1, b=4, and c=5. So, the equation for the axis of symmetry is given by

x = −(4)/2(-1)

x = - 4/-2

x = 2

The equation of the axis of symmetry for g(x)=-x^{2}+4x+5 is x = 2.

The x coordinate of the vertex is the same:

h = 2

The y coordinate of the vertex is :

k = g(h)

k = -(h)^{2} + 4(h) + 5

k = -(2)^{2} + 4(2) + 5

k = -4 + 8 + 5

k = 9

Therefore, the vertex is (2 , 9)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = -(0)^{2} + 4(0) + 5

y = 0 + 0 + 5

y = 5

Therefore, Axis of symmetry is x = 2

Vertex is ( 2 , 9 )

Y- intercept is 5.

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