How do you find the vertex of y=x^2+10x-21?
The first derivitive is the slope
of the curve at any point. y' = 2x + 10
When the slope is zero, it means
the curve is neither increasing nor
decreasing, so set the first derivitive
equal to zero and solve for x 2x + 10 = 0
2x = –10
x = –5 This is the x-coordinate.
Substitute –5 back into the
original equation y = x2 + 10x – 21
y = (–5)2 + (10)(–5) – 21
y = 25 – 50 – 21
y = –46 This is the y-coordinate.
So the vertex of the parabola is at (–5 , –46)
You can take the original equation y=x^2+10x-21
to the Desmos Graphing Calculator and see it
drawn. That's how I checked my answer.