Exercise 93 Page 88

We want to draw the graph of the given quadratic function. Note that the function is already written in vertex form, y=a(x-h)^2+k, where a, h, and k are either positive or negative numbers. y=2(x-4)^2-3 ⇕ y=2(x-4)^2+(-3) To draw the graph, we will follow four steps.

1. Identify the constants a, h, and k.
2. Plot the vertex (h,k) and draw the axis of symmetry x=h.
3. Plot any point on the curve and its reflection across the axis of symmetry.
4. Sketch the curve.

   Let's get started.

   Step 1

   We will first identify the constants a, h, and k. Recall that if a<0, the parabola will open downwards. Conversely, if a>0, the parabola will open upwards. Vertex Form:& y= a(x- h)^2+k Function:& y= 2(x- 4)^2+(-3) We can see that a= 2, h= 4, and k=-3. Since a is greater than 0, the parabola will open upwards.

   Step 2

   Let's now plot the vertex ( h,k) and draw the axis of symmetry x= h. Since we already know the values of h and k, we know that the vertex is ( 4,-3). Therefore, the axis of symmetry is the vertical line x= 4.

   

   Step 3

   We will now plot a point on the curve by choosing an x-value and calculating its corresponding y-value. Let's try x=5.
   y=2(x-4)^2-3

   Substitute

   x= 5

   y=2( 5-4)^2-3

   ▼

   Simplify right-hand side

   SubTerm

   Subtract term

   y=2(1)^2-3

   BaseOne

   1^a=1

   y=2(1)-3

   MultByOne

   a * 1=a

   y=2-3

   SubTerm

   Subtract term

   y=-1
   When x=5, we have y=-1. Thus, the point (5,-1) lies on the curve. Let's plot this point and reflect it across the axis of symmetry.
   

   Note that both points have the same y-coordinate.

   Step 4

   Finally, we will sketch the parabola which passes through the three points. Remember not to use a straightedge for this!