Maths-

General

Easy

Question

# Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . H(x)= -3x^{2}+7x+1

Hint:

Maths-

General

Easy

Question

Hint:

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 (

The

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

In H(x)= -3x

x = −(7)/2(-3)

x = - 7/-6

x = 7/6

The equation of the axis of symmetry for H(x)= -3x

The x coordinate of the vertex is the same:

h = 7/6

The y coordinate of the vertex is :

k = H(h)

k = -3(h)

k = -3(7/6)

k = -(49/12) + (49/6) + 1

k = 5.083

Therefore, the vertex is (1.167 , 5.083)

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

y = -3(0)

y = 0 + 0 + 1

y = 1

Therefore, Axis of symmetry is x = 7/6

Vertex is ( 1.167 , 5.083 )

Y- intercept is 1.