# 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?

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).