The extreme point of a parabola is called a quad.
Valuable information about the function can be found in the graph of a parabola.
There are constants where [latex]a, b, and c are.
The sign on the coefficients affects whether the graph opens or closes.The graph makes a frown and a smile if it opens up.This is displayed below.
The direction of the parabola is determined by the sign on the coefficients.
The shape and placement of parabolas are recognizable.
The parabola has an extreme point called the vertex.If the parabola opens, the lowest point on the graph is the minimum value of the function.The maximum value is the highest point on the graph if the parabola opens down.The graph has a turning point on it.
The axis of symmetry is parallel to the y- axis.The axis of symmetry is a horizontal line.
The y-Intercept is the point at which the parabola crosses.There can't be more than one point for the graph of a function.The curve wouldn't be a function if there were two values for one value.
The points at which the parabola crosses are known as the x-Intercepts.If they exist, the x-Intercepts represent the zeros and roots of the function.There could be zero, one, or two intercepts.The location of the graph affects the number ofcepts.
There is a possibility that a parabola can have no x-Intercepts.
If the function is set to zero, the result is a quadratic equation.The roots of the function are the solutions to the equation.These are the same roots that can be seen in the parabola.
The vertex always falls between the roots for parabolas with twocepts.Due to the fact that parabolas are symmetrical, the [latex]x is in the middle of the two roots.
The roots of a function can be found using a formula.The roots of a function can be seen graphically.Two different methods can be used to reach the same values, and we will see how they are related.
The function is graphed below.It is possible to solve for its roots graphically and algebraically.
The graph shows the parabola on the plane, including the points where it crosses the x- axis.
The parabola intersects the [latex]x at two points.The roots of the function are indicated by thecepts of a parabola.There are roots at [latex]x.
The roots of [latex]f(x) are solved with the quadratic formula.
The quadratic equation sets the expression to zero.
The formula can be used to find the values for which this statement is true.We have the coefficients for the given equation.
There are two possible values for x.
These reduce to 2 and 1 respectively.When we solved for roots graphically, we found the same values.
Find the roots of the function.There are two ways to solve graphically and algebraically.
There is a graph of x2 - 4x + 4.There is a graph of the above function.
The function does not intersect the [latex]x axis.It has no real roots.
We can verify it.First, identify the values for the coefficients.
There is a number in the formula that is not a real number.There are no roots for the given function.We have arrived at the same conclusion.
Explain the meanings of the constants.
It is very easy to tell where a quadratic is located when it is written in a form called a vertex form.The form is given by:
The edge is latex.If the form were [latex]f(x) it would be the vertex.The speed of increase or decrease of the parabola is controlled by the coefficients as before.
If you want to make a standard form of a quadrangular form, you can use the square and combine like terms.The quadratic is an example.
It's more difficult to convert from standard form to a different form.The process is called tidying the square.
Suppose you want to write in the form of a graph.The one we call [latex]a is the one with the lowest coefficients.When this is the case, we look at the coefficients on [latex]x and take half of them.We square that number.For this example, we divide [latex]4 by 2 and then square it to get it.
We didn't actually change our function because we added and subtracted 4.The expression in the parentheses is a square.Our equation is now in a form that is called a 'latex'.Latex
It is more difficult to convert standard form to vertex form when the coefficients are not the same.We can still use the technique, but must be careful to factor out the latex as in the following example.
Consider [latex]y 2x, 12x and 5x.We factor out the coefficients from the first two terms.
The square is completed within the parentheses.Half of [latex]6 is 3 and 2.We add and subtract from the parentheses.
Explain the meaning of the constants for a standard equation.
The shape and placement of the function's graph can be affected by the coefficients in a standard form.
The speed of increase and decrease of the function is controlled by the coefficients.A larger positive makes the function increase and the graph thinner.
The speed of increase of the parabola is controlled by the coefficients.The black curve is larger than the blue curve.The black curve is thinner because it's bigger than the blue curve.
Whether the parabola opens upward or downward is controlled by latex.The parabola can open upward or downward depending on the coefficients.
The graph of [latex]y=3x2 is the blue parabola.Since [latex]a=3>0, it opens upward.The black parabola is a graph.Since [latex]a is 30, it opens downward.Latex.
The axis of symmetry of the parabola is controlled by the coefficients.The axis of symmetry for a parabola is given.
Consider the parabola shown below.The axis of symmetry is: