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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:

### 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: ( 1.167 , 5.083 )

### 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 H(x)= -3x^{2}+7x+1, a= -3, b=7, and c=1. So, the equation for the axis of symmetry is given by

x = −(7)/2(-3)

x = - 7/-6

x = 7/6

The equation of the axis of symmetry for H(x)= -3x^{2}+7x+1 is x = 7/6.

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)^{2} + 7(h) + 1

k = -3(7/6)^{2} + 7(7/6) + 1

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)^{2} + 7(0) + 1

y = 0 + 0 + 1

y = 1

Therefore, Axis of symmetry is x = 7/6

Vertex is ( 1.167 , 5.083 )

Y- intercept is 1.

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