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.
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.
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.
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.
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.
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vertex
Depending on the graph, for a quadratic function the salient features are: X- intercept, Y-intercept and the turning point.
Some do and some don't. It's possible but not necessary.
It will have two equal roots.
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)
It is a turning point. It lies on the axis of symmetry.
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.
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.
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.
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.
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If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.