Answer:
It can be determined if a quadratic function given in standard form has a minimum or maximum value from the sign of the coefficient "a" of the function. A positive value of "a" indicates the presence of a minimum point while a negative value of "a" indicates the presence of a maximum point
Step-by-step explanation:
The function that describes a parabola is a quadratic function
The standard form of a quadratic function is given as follows;
f(x) = a·(x - h)² + k, where "a" ≠ 0
When the value of part of the function a·x² after expansion is responsible for the curved shape of the function and the sign of the constant "a", determines weather the the curve opens up or is "u-shaped" or opens down or is "n-shaped"
When "a" is negative, the parabola downwards, thereby having a n-shape and therefore it has a maximum point (maximum value of the y-coordinate) at the top of the curve
When "a" is positive, the parabola opens upwards having a "u-shape" and therefore, has a minimum point (minimum value of the y-coordinate) at the top of the curve.
Is this calculus or something?
Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply.
(x + 1)
(2x + 1)
(x + 2)
(5x + 1)
<span>(5x – 2)
Solution :
By multiplying (5x - 2) and (x + 2), the given trinomial will be obtain as follow.
</span>(5x - 2) * (x + 2) = (5x * x) + (5x * 2) - (2 * x) - (2 * 2)
= <span>5x^2 + 10x - 2x - 4
= </span>5x^2 + 8x - 4
Thats correct for first derivative ( use the chain rule)
For the second derivative you use product rule and the chain rule
= 2x * 2x e^(x^2) + 2 e^(x^2)
= 4x^2 e^(x^2) + 2e^(x^2)
you are right
Change it to make y= on one side
3x + 4y = 1
4y = -3x + 1
y = -3/4x + 1/4
The slope is the fraction before x
The slope is -3/4
