What is a quadratic equation with 2 solutions?

What is a quadratic equation with 2 solutions?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.

How do you know if a quadratic has 2 solutions?

If b2 – 4ac is positive (>0) then we have 2 solutions. If b2 – 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b2 – 4ac is less than 0 we have no solutions.

What is the graph of quadratic equation in two variables?

The graph of the function in one variable f(x) = x2 is called a parabola. To recap, the graph of f(x) = x2 in the plane is the same set as the set of solutions of the quadratic equation in two variables given by the equation y = x2. That is, the parabola below is a conic.

Do all quadratic equations have 2 solutions?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

What is a quadratic equation graph?

Graphs. A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape.

How do you know how many solutions a quadratic graph has?

Given a quadratic equation ax2 + bx + c = 0, plug the coefficients into the expression b2 – 4ac to see what results:

1. If you get a positive number, the quadratic will have two unique solutions.
2. If you get 0, the quadratic will have exactly one solution, a double root.

What equation has both 2 and as solutions?

quadratic equation
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.

How do you find the equation of a quadratic graph?

Key Points

1. The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y -axis.
2. The coefficients a,b, and c in the equation y=ax2+bx+c y = a x 2 + b x + c control various facets of what the parabola looks like when graphed.

Why do quadratic equations have two solutions?

A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.

How do you determine if a quadratic equation is rational?

Interpret the Discriminant of a Quadratic Equation The discriminant is negative, so the equation has two non-real solutions. The discriminant is 0, so the equation has a double root. If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational.

What is the graph of a rational function?

Rational functions are of the form y=f(x) , where f(x) is a rational expression . The graphs of the rational functions can be difficult to draw. To sketch a graph of a rational function, you can start by finding the asymptotes and intercepts.

How to use a graph to solve a quadratic equation?

Examples of how to use the graph of a quadratic function to solve a quadratic equation: Two solutions, one solution and no solution. 1. Use the graph of y = x 2 + x – 6 to solve x 2 + x – 6 = 0. 2. Use the graph of y = -x 2 + 4 to solve -x 2 + 4 = 0.

When do you have two solutions for a quadratic function?

Compared to the other methods, the graphical method only gives an estimate to the solution (s). If the graph of the quadratic function crosses the x-axis at two points then we have two solutions. If the graph touches the x-axis at one point then we have one solution.

When does a quadratic equation have two roots?

A quadratic equation has two roots if its graph has two x-intercepts. A quadratic equation has one root it its graph has one x-intercept. A quadratic equation has no real solutions if its graph has no x-intercepts. Here you can get a visual of your quadratic function.

Is there a graphical solution to the equation x 2 + 4x + 8?

Solve the equation x 2 + 4x + 8 = 0 using the graphical method. Notice that the graph does not cross or touch the x-axis. This means that the equation x 2 + 4x + 8 = 0 does not have any real solution (or roots). Recall that in the quadratic formula, the discriminant b 2 – 4ac, is negative when there are no real solution (or roots).