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How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is zero?
It will touch it at exactly 1 point. If a quadratic function is given as f(x) = ax2 + bx + c, let the discriminant be denoted as D. Then the graph of y = f(x) will cross the x-axis at the x-values x = (-b + sqrt(D))/(2a) and x = (-b - sqrt(D))/(2a). When the discriminant D = 0, these 2 x-values are actually the same. Thus the graph will touch the x-axis only once.
What is the maximum number of times the graph of the quadratic function can cross the x-axis?
Two.
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 do you find the discriminant on a graph?
The discriminant is the expression under the square root of the quadratic formula.For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:x = (-b +- sqrt(b2 - 4ac)) / (2a).So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.(b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.(b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.(b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.
If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis time s?
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
If the discriminant is negative the graph of the quadratic function will cross or touch the x-axis how many times?
It would not touch or intersect the x-axis at all.
How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?
Once.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
If the discriminant is zero the graph of a quadratic function will cross or touch the x-axis time s?
It will touch the x-axis and not cross it.
If the discriminant is zero the graph of a Quadratic function will cross or touch the x-axis time(s)?
It will touch the x-axis once.
How many times will The graph of a quadratic function crosses the x-axis twice?
A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.
When the discriminant is negative will the graph of the function cross or touch?
The graph will cross the y-axis once but will not cross or touch the x-axis.
The graph of a certain quadratic function does not cross the x-axis Which of the following are possible values for the discriminant Check all that apply?
-1 -18 -25 -7
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is zero?
It will touch it at exactly 1 point. If a quadratic function is given as f(x) = ax2 + bx + c, let the discriminant be denoted as D. Then the graph of y = f(x) will cross the x-axis at the x-values x = (-b + sqrt(D))/(2a) and x = (-b - sqrt(D))/(2a). When the discriminant D = 0, these 2 x-values are actually the same. Thus the graph will touch the x-axis only once.
What is the graph of a function if the discrimanent is zero?
When the discriminant of a quadratic function is zero, the graph of the function is a parabola that touches the x-axis at a single point, known as a double root. This means that the function has exactly one real solution, and the vertex of the parabola is located on the x-axis. In this case, the parabola opens either upwards or downwards but does not cross the x-axis.
