Exercise 22 Page 61

To draw the graph of the given quadratic function, written in standard form, we must start by identifying the values of a, b, and c. y=3x^2-6x+4 ⇔ y=3x^2+(- 6)x+4 We can see that a=3, b=- 6, and c=4. Now, we will follow four steps to graph the function.

1. Find the axis of symmetry.
2. Calculate the vertex.
3. Identify the y-intercept and its reflection across the axis of symmetry.
4. Connect the points with a parabola.

   Finding the Axis of Symmetry

   The axis of symmetry is a vertical line with equation x=- b2a. Since we already know the values of a and b, we can substitute them into the formula.
   x=- b/2a

   SubstituteII

   a= 3, b= - 6

   x=- - 6/2(3)

   ▼

   Simplify right-hand side

   Multiply

   Multiply

   x=- - 6/6

   RemoveNegFracAndNum

   - - a/b= a/b

   x=6/6

   CalcQuot

   Calculate quotient

   x=1
   The axis of symmetry of the parabola is the vertical line with equation x=1.

   Calculating the Vertex

   Note that the formula for the x-coordinate of the vertex is the same as the formula for the axis of symmetry, which is x=1. To find the y-coordinate of the vertex, we need to substitute 1 for x in the given equation.
   y=3x^2-6x+4

   Substitute

   x= 1

   y=3( 1)^2-6( 1)+4

   ▼

   Simplify right-hand side

   CalcPow

   Calculate power

   y=3(1)-6(1)+4

   Multiply

   Multiply

   y=3-6+4

   AddSubTerms

   Add and subtract terms

   y=1
   We found the y-coordinate, and now we know that the vertex is ( 1,1).

   Identifying the y-intercept and its Reflection

   The y-intercept of the graph of a quadratic function written in standard form is given by the value of c. Thus, the point where our graph intercepts the y-axis is (0,4). Let's plot this point and its reflection across the axis of symmetry.

   

   Connecting the Points

   We can now draw the graph of the function. Since a=3, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.