Exercise 14 Page 61

We want to draw the graph of the given quadratic function. To do so, we will rewrite it in vertex form, f(x)=a(x-h)^2+k, where a, h, and k are either positive or negative numbers. g(x)=0.75x^2-5 ⇕ g(x)=0.75(x-0)^2-5 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:& f(x)= a(x- h)^2+k Function:& g(x)= 0.75(x- 0)^2+(- 5) We can see that a= 0.75, h= 0, and k=- 5. 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 ( 0,- 5). Therefore, the axis of symmetry is the vertical line x= 0.

   

   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=4.
   g(x)=0.75(x)^2-5

   Substitute

   x= 4

   g( 4)=0.75( 4)^2-5

   ▼

   Simplify right-hand side

   CalcPow

   Calculate power

   g(4)=0.75(16)-5

   Multiply

   Multiply

   g(4)=12-5

   SubTerm

   Subtract term

   g(4)=7
   When x=4, we have y=7. Thus, the point (4,7) 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!