Do not use calculus guys.

Use the straight way to have the correct answer

what's the solution Mr.Carcass?

Those provided above by @jwolbrum are a perfect example of a flexible approach.

Nothing to add to those Sir

while using ""Plugging in and verifying that we have real roots" method what the mean that we have non-imaginary roots?

A function is defined by \(f(x) = x^2 + 4x – 5\).

What is the minimum value of \(f(x)\)?

\(f(x) = x^2 + 4x – 5 = (x+2)^2 -9\).
Since \((x+2)^2 =0\) for f(x) to be minimum
Minimum value of f(x) = -9

E

Given that \(f(x) = x^2 + 4x – 5\) and we need to find the minimum value of \(f(x)\)

\(f(x) = x^2 + 4x – 5\) = \(x^2 + 4x + 4 - 4 – 5\) = \(x^2 + 2*2x + 2^2 -9\) = \((x+2)^2 - 9\)

Now, we know that a Square of a number is always \(\geq\) 0
=> Minimum value of \((x+2)^2\) = 0
=> Minimum vale of f(x) = \((x+2)^2 - 9\) = 0-9 = -9

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

What is the formula to find maximum?

The way you solved it is much faster than my way, but I wanted to share my way in case it helped.

My instinct was to factor, so I did that, and found that it was (x+5)(x-1). Then, recognized it was a parabola, so the x-midpoint of the parabola's x-intercepts, is the x value when y is at its minimum.

The x-intercepts are x=-5 and x=1. Midpoint is -2. Plug in -2 into the equation and you get the answer, -9 (E).

My instincts told me if we plug values less than zero, viz -1,-2,-3 we could get the answer quickly

If x = -1 f(x) = -8
If x = -2 f(x) = -9

We can stop at this point since -9 is the lowest value in the choices. The answer is Choice E.

If we proceed further

if x = -3 f(x) = -8

Note that f(x) decreases in value and increases once again (because it is a parabola). So it will never come back to -9 again. But we can try one more value:

if x = -4 f(x) = -5

So we can be sure -9 is the lowest value. This method required simple mental calculation and is probably faster than the other methods depending on your mental skills.

Chaithraln2499: The maximum value will be infinity as the graph is a quadratic equation and as x increases to bigger values the value of the function will reach infinity.

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