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How would you use intercepts to find the vertex in a quadratic equation with two x intercepts?
The vertex must be half way between the two x intercepts
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.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What is the shape of the function y 16x x2?
Restate the question: What is the shape of the function y = 16x - x2?Since the function highest power is a square, this is a quadratic function, and the graph is a parabola. Maybe that's all you wanted to know, but here's the rest of the story:Since the coefficient of x is negative (it's -1), the parabola opens down (the shape is an upside down 'u').The x-intercepts are found by factoring and solving: 16x-x2 = 0 -> x(16-x) = 0 -> x=0 or [16-x=0 -> 16=x]. The graph crosses the x-axis at 0 and 16.The top of the parabola will be where x=8 (half-way between the intercepts). Substitute in y = 16x - x2 = 16(8) - (8)2 = 128 - 64 = 64.The graph passes through (0,0), (8, 64), and (16,0).
What is the difference between coordinate system and coordinate plane?
The coordinate system can be in any number of dimensions whereas the coordinate plane is a 2-dimensional concept.
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the lies exactly halfway between the two x-intercepts?
Exactly halfway
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the vertex lies between the two x-intercepts?
The x co-ordinate of a quadratic lies exactly halfway between the two x-intercepts, assuming they exist. Alternatively, the x co-ordinate can be found using the formula -B/(2A), when the function is in the form, y = Axx + Bx + C.
How would you use intercepts to find the vertex in a quadratic equation with two x intercepts?
The vertex must be half way between the two x intercepts
How are factors graphs and zeros of quadratic functions related?
The factors of a quadratic function are expressed in the form ( f(x) = a(x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the roots or zeros of the function. These zeros are the values of ( x ) for which the function equals zero, meaning they correspond to the points where the graph of the quadratic intersects the x-axis. Thus, the factors directly indicate the x-intercepts of the quadratic graph, highlighting the relationship between the algebraic and graphical representations of the function.
The difference between Quadratic function and quadratic equation?
dunctions are not set equal to a value
What is the difference between a linear and quadratic function?
A linear function is a line where a quadratic function is a curve. In general, y=mx+b is linear and y=ax^2+bx+c is quadratic.
What are the similarities between quadratic function and linear function?
Both are polynomials. They are continuous and are differentiable.
What is the difference between x-intercepts of a function and zeros of a function?
Assuming it is a function of "x", those are two different names for the same thing.
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.
What are comparisons between a cubic and quadratic function?
They are both polynomial functions. A quadratic is of order 2 while a cubic is of order 3. A cubic MUST have a real root, a quadratic need not.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What are the similarities between quadratic function and cubic function?
Both quadratic and cubic functions are polynomial functions, meaning they can be expressed in the form of ( ax^n + bx^{n-1} + \ldots ) where ( a ) is a non-zero coefficient and ( n ) is a non-negative integer. They both exhibit smooth, continuous curves and can have real or complex roots. Additionally, both types of functions can model a variety of real-world phenomena and can be analyzed using similar techniques, such as finding their vertices, intercepts, and analyzing their behavior at infinity.
