How do you use the important points to sketch the graph of # f(x)= x^2+10x-8#?

Question

Isaiah Anthony · Accepted Answer

I would complete the square.

Completing the square will tell us the roots first of all, a nice basis to sketch the graph. #therefore# #f(x) = (x+5)^2 -25-8# #=(x+5)^2-33# Now we solve the completed square... #(x+5)^2-33=0# #(x+5)^2=33# #(x+5)= +-sqrt33# #x=-5+-sqrt33# Now we have our two roots. The completed square also gives a minimum (as the quadratic is a positive function). #(x+5)^2-33# has a minimum turning point at #(-5,-33)# Lastly, the constant of the equation will give us the y intercept, in this case a y intercept at #(0,-8)# Now we sketch a graph, by plotting these points and drawing a nice smooth curve. graph{y=x^2 +10x-8 [-14.68, 5.32, -37.21, -27.21]}

Genesis Allen · Answer

undefined To sketch the graph of $ f(x) = x^2 + 10x - 8 $, you can follow these steps:

1. Identify the important points: 
   - Vertex: Use the formula $ x = \frac{-b}{2a} $ to find the x-coordinate of the vertex, where $ a = 1 $ and $ b = 10 $. Then plug this x-value into the function to find the corresponding y-value.
   - x-intercepts: Set $ f(x) = 0 $ and solve for x.
   - y-intercept: Plug $ x = 0 $ into the function to find the y-coordinate.

2. Plot the important points on the coordinate plane.

3. Determine the direction of the parabola by considering the coefficient of $ x^2 $. Since $ a = 1 $ (positive), the parabola opens upwards.

4. Sketch the curve through the important points, making sure it curves smoothly.

5. Optionally, you can find additional points by choosing other x-values and calculating the corresponding y-values using the function. This helps in ensuring the accuracy of the sketch.