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Yes, the product of two linear functions is always a quadratic function. A linear function can be expressed in the form ( f(x) = ax + b ) and ( g(x) = cx + d ). When you multiply these two functions, ( f(x) \cdot g(x) = (ax + b)(cx + d) ), the result is a polynomial of degree 2, which is the definition of a quadratic function.
What else can I help you with?
Is the quadratic equation always a function?
Yes it is.
Is a graph of a quadratic function always a parabola?
No. It can also be a circle, ellipse or hyperbola.
Once you have reduced a polynomial to a cubic function you can always use the quadratic formula to finish the problem?
false
Once you have reduced a polynomial to a quartic function you can always use the quadratic formula to finish the problem?
false
Can a quadratic function have a range of negative infinity to infinity?
No, a quadratic function cannot have a range of negative infinity to infinity. The graph of a quadratic function is a parabola, which opens either upwards or downwards. If it opens upwards, the range is from the minimum value to positive infinity, and if it opens downwards, the range is from negative infinity to the maximum value. Therefore, the range is always limited to a specific interval rather than covering all real numbers.
Is the quadratic equation always a function?
Yes it is.
Once you have reduced a polynomial to a quadratic function you can always use the quadratic formula to finish the problem?
True
What is the relation quadratic equation to linear equation?
The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).
What is the difference between quadratic function and quadratic formula?
A quadratic function is a function where a variable is raised to the second degree (2). Examples would be x2, or for more complexity, 2x2+4x+16. The quadratic formula is a way of finding the roots of a quadratic function, or where the parabola crosses the x-axis. There are many ways of finding roots, but the quadratic formula will always work for any quadratic function. In the form ax2+bx+c, the Quadratic Formula looks like this: x=-b±√b2-4ac _________ 2a The plus-minus means that there can 2 solutions.
Is a graph of a quadratic function always a parabola?
No. It can also be a circle, ellipse or hyperbola.
Is a function is always a relation?
Yes. Functions are always relations, but relations are not always functions.
Once you have reduced a polynomial to a cubic function you can always use the quadratic formula to finish the problem?
false
Once you have reduced a polynomial to a quartic function you can always use the quadratic formula to finish the problem?
false
What different information do you get from vertex form and quadratic equation in standard form?
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
Is inverse of a function always positive?
No.Some functions have no inverse.
The sum of two quadratic functions will always be quadratic?
No. While the sum of two qudratics cannot have a power greater than two, it could have a power of 2, 1 or 0. x2 + 1 is one quadratic (2-x)(2+x) is another quadratic. Their sum is 1, a constant (power = 0).
Are all linear equations functions Is there an instance when a linear equation is not a function?
Linear equations are always functions.
