What real value of \(t\) produces the smallest value of the quadratic \(t^2 -9t - 36 \)?

Hey @pinklemonade!

Use the factoring method to get -3 as the answer for t.

Cheers!

The "t" that produces the smallest value is at the vertex of this parabola.....this is

- (-9) / [ -2 *1 ] = 9/2 = 4.5

See the graph here : (I've used x instead of t....but....same idea) :

https://www.desmos.com/calculator/jzlppgwsly

@CPhill, are you sure it is 4.5?

Yeah....look at the graph I cited in my answer

When t = 4.5 the graph is at its minimum = -56.25

So....t =4.5 produces the minimum value of the quadratic