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The graph of a quadratic function has it's turning point on the x-axis. How many roots does the function have?
If the turning point of a quadratic function is on the x-axis, it means the vertex of the parabola touches the x-axis, indicating that the function has exactly one root. This occurs when the discriminant of the quadratic equation is zero, resulting in a double root at the turning point. Therefore, the function has one real root.
What else can I help you with?
How does the graph show that the quadratic is a function?
No vertical line will intersect the graph in more than one point. The fundamental flaw is that no graph can show that it does not happen beyond the domain of the graph.
What is the turning point of a graph called?
The turning point of a graph is called a "critical point" or "extremum." In calculus, these points occur where the derivative of a function is zero or undefined, indicating a local maximum or minimum. At these points, the graph changes direction, which can represent peaks or valleys in the function's behavior.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
How do you find gradient on a quadratic graph?
To find the gradient on a quadratic graph, you first need to determine the derivative of the quadratic function, which is typically in the form (y = ax^2 + bx + c). The derivative, (y' = 2ax + b), represents the gradient at any point (x) on the curve. By substituting a specific (x) value into the derivative, you can find the gradient at that particular point on the graph. This gradient indicates the slope of the tangent line to the curve at the chosen point.
If the graph of quadratic function x has a minimum point and intersects the axis of x at 4 and m If the axis of symmetry of the graph is x equal to 5 state the value m and hence state the function x?
...i need the answer to that too...
What name is given to the turning point also known as the maximum or minimum of the graph of a quadratic function?
vertex
How do you find the salient feature in a graph?
Depending on the graph, for a quadratic function the salient features are: X- intercept, Y-intercept and the turning point.
Is the graph of a quadratic function contains the point 0 0?
Some do and some don't. It's possible but not necessary.
When the graph of a quadratic equation has its turning point on the x-axis how many roots does it have?
It will have two equal roots.
What is the turning point in the graph of a quadratic function?
The answer depends on the form in which the quadratic function is given. If it is y = ax2 + bx + c then the x-coordinate of the turning point is -b/(2a)
What things are significant about the vertex of a quadratic function?
It is a turning point. It lies on the axis of symmetry.
What does it mean when the graph of a quadratic function crosses the x axis twice?
When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots. If the graph touches the x-axis at one point the quadratic has 1 repeated root. If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.
How does the graph show that the quadratic is a function?
No vertical line will intersect the graph in more than one point. The fundamental flaw is that no graph can show that it does not happen beyond the domain of the graph.
What is the turning point of a graph called?
The turning point of a graph is called a "critical point" or "extremum." In calculus, these points occur where the derivative of a function is zero or undefined, indicating a local maximum or minimum. At these points, the graph changes direction, which can represent peaks or valleys in the function's behavior.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
How do you find gradient on a quadratic graph?
To find the gradient on a quadratic graph, you first need to determine the derivative of the quadratic function, which is typically in the form (y = ax^2 + bx + c). The derivative, (y' = 2ax + b), represents the gradient at any point (x) on the curve. By substituting a specific (x) value into the derivative, you can find the gradient at that particular point on the graph. This gradient indicates the slope of the tangent line to the curve at the chosen point.
If the graph of quadratic function x has a minimum point and intersects the axis of x at 4 and m If the axis of symmetry of the graph is x equal to 5 state the value m and hence state the function x?
...i need the answer to that too...
