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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.
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.
If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis?
No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.
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.
Can the graph of a function yfx always cross the y-axis?
No. It depends on the function f.
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.
How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?
Once.
What does the rule for a quadratic function tell you about how the graph of the function will look?
If the quadratic function is written as ax2 + bx + c then if a > 0 the function is cup shaped and if a < 0 it is cap shaped. (if a = 0 it is not a quadratic) if b2 > 4ac then the equation crosses the x-axis twice. if b2 = 4ac then the equation touches the x-axis (is a tangent to it). if b2 < 4ac then the equation does not cross the x-axis.
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.
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.
When the coefficient of x2 is negative?
When the coefficient of ( x^2 ) is negative in a quadratic equation, the parabola opens downward. This means that the vertex of the parabola represents a maximum point, and the value of the function decreases on either side of the vertex. Consequently, the graph will touch or cross the x-axis at most twice, indicating that the quadratic can have zero, one, or two real roots.
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.
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.
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
If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis?
No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.
