SOLUTION: Could someone please show me how to find the vertex, the line of symmetry, the maximum or minimum of the quadratic function, and graph the function,what is the equation of the line

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Could someone please show me how to find the vertex, the line of symmetry, the maximum or minimum of the quadratic function, and graph the function,what is the equation of the line      Log On


   

Question 526824: Could someone please show me how to find the vertex, the line of symmetry, the maximum or minimum of the quadratic function, and graph the function,what is the equation of the line of symmetry? f(x)=x^2-12x-5
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex, Line of symmetry (LOS), Maximum (or minimum).
f%28x%29+=+x%5E2-12x-5
1) The x-coordinate of the vertex is given by:
x+=+-b%2F2a The a and b come from the general form of the quadratic equation: f%28x%29+=+ax%5E2%2Bbx%2Bc, so a = 1 and b = -12.
x+=+-%28-12%29%2F2%281%29
x+=+6 The y-coordinate is found by substituting this value of into the given quadratic equation and solving for y, thus: (Change f(x) to y).
y+=+x%5E2-12x-5 Substitute x = 6.
y+=+%286%29%5E2-12%286%29-5 Evaluate.
y+=+36-72-6
y+=+-41
The vertex is at (6, -41)
The equation of the line of symmetry is simply:
x+=+6
This equation, when graphed, will show a parabola that opens upwards and therefore its vertex will be at its minimum point.
You can tell which way the parabola opens by inspecting the coefficient of the x%5E2 term (a):
If a is positive, the parabola opens upwards.
If a is negative, the parabola opens downwards. Here's the graph.
graph%28400%2C400%2C-5%2C15%2C-45%2C5%2Cx%5E2-12x-5%29