Exercise 2 Page 224

We want to draw the graph of the given quadratic function. To do so, we will rewrite it in vertex form y=a(x-h)^2+k, and highlight the coefficients. y=(x+8)^2-3 ⇕ y=1(x-(- 8))^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= 1(x-( - 8))^2+( - 3) We can see that a= 1, h= - 8, and k= - 3. Since a is greater than 0, the parabola will open upwards.

   Step 2

   Recall that the axis of symmetry is a vertical line that passes through the vertex ( h, k). As a result, it takes the form x= h. Since we already know the values of h and k, we know that the vertex is ( - 8, - 3) and the axis of symmetry is x= - 8.

   

   Step 3

   We will now plot a point on the curve by choosing an arbitrary x-value and calculating its corresponding y-value. Let's try x=- 6.
   y=(x+8)^2 -3

   Substitute

   x= - 6

   y=( - 6+8)^2 -3

   ▼

   Simplify right-hand side

   AddTerms

   Add terms

   y=(2)^2-3

   CalcPow

   Calculate power

   y=4-3

   SubTerm

   Subtract term

   y=1
   When x=- 6, we have y=1. Thus, the point (- 6,1) lies on the curve. Let's plot this point and its reflection 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 straight edge for this!