Question

Shiori is working on a stem project and her model is represented by the quadratic function below. She eventually wants to build a 3D model si she needs to understand each part of the function . She is trying to find the coordinate of the vertex of the following function and determine whether the graph opens up or down. F(x)=3x^2-2x-71. What are the coordinates of the vertex of the parabola of the function. There are several wars to determine this answer but state clearly all the steps you look to find the solution.2.Just by looking at the equation (without graphing it) does the graph open up or down(How do you know).3.what does the -7 tell you about the parabola specifically.

Answer 1

1) To get the vertex of the function, the formulae is given as:

`x=-(b)/(2a)`

This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.

`x=(-(-2))/(2(3))=(1)/(3)=0.333333`

To get the y coordinate, we substitute this x value into the original equation.

`f(x)\text{ = 3(}(1)/(3))^2-2((1)/(3))-7=(-22)/(3)=-7.333333`

The coordinates of the the vertex (0.33, -7.33)

2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.

3) The -7 tells us that the graph cuts the vertical axis at -7.