Write a quadratic function in standard form with Zeros 6 and -1
y = (x-6)(x+1)
Now expand it out to standard form.
To write a quadratic function in standard form with zeros 6 and -1, we can use the zero product property.
The zero product property states that if a quadratic function is equal to zero, then one or both of its factors must be equal to zero.
So, if the zeros are 6 and -1, the factors of the quadratic function are (x - 6) and (x + 1).
To find the quadratic function, we can multiply these factors:
(x - 6)(x + 1) = x^2 - 6x + x - 6 = x^2 - 5x - 6
Therefore, the quadratic function in standard form with zeros 6 and -1 is f(x) = x^2 - 5x - 6.
To write a quadratic function in standard form with zeros 6 and -1, we can use the zero-product property. The zero-product property states that if a quadratic equation has two zeros, say x = a and x = b, then the equation of the quadratic function can be written in the form:
f(x) = (x - a)(x - b)
In this case, the zeros are 6 and -1. So, we have:
f(x) = (x - 6)(x - (-1))
To simplify this equation, we need to multiply the two binomials:
f(x) = (x - 6)(x + 1)
Using the distributive property, we expand the equation:
f(x) = x(x) + x(1) - 6(x) - 6(1)
Simplifying further:
f(x) = x^2 + x - 6x - 6
Combining like terms:
f(x) = x^2 - 5x - 6
So, the quadratic function in standard form with zeros 6 and -1 is f(x) = x^2 - 5x - 6.