9th-11th Grade Math - Quadratic Functions | Inside Mathematics (2024)

FAQs

What is the easiest way to solve quadratic functions? ›

Factoring is the first of the three methods of solving quadratic equations. It is often the fastest way to solve a quadratic equation, so usually should be attempted before any other method. This method relies on the fact that if two expressions multiply to zero, then at least one of them must be zero.

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, (b [ 2 ] - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Quadratic equation may have infinitely many solutions. But only two roots or zeros. Because we can put any random value of x(x belongs to R), we can get corresponding value of y. Generally, solutions of an equation are nothing but points which are on the curve which is corresponding to that equation.

The quadratic equation of the standard form ax2+bx+c has two solutions. The solutions or roots of quadratic equations can be positive/negative, same/distinct, and real or imaginary.

In other words, the quadratic formula is simply just ax^2+bx+c = 0 in terms of x. So the roots of ax^2+bx+c = 0 would just be the quadratic equation, which is: (-b+-√b^2-4ac) / 2a. Hope this helped!

Answer: If a quadratic equation has exactly one real number solution, then the value of its discriminant is always zero. A quadratic equation in variable x is of the form ax² + bx + c = 0, where a ≠ 0.

The general form of a quadratic function is given as: f(x) = ax² + bx + c, where a, b, and c are real numbers with a ≠ 0. The roots of the quadratic function f(x) can be calculated using the formula of the quadratic function which is: x = [ -b ± √(b² - 4ac) ] / 2a.

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

9th-11th Grade Math - Quadratic Functions.

How to tell how many solutions a quadratic equation has without solving? ›

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.

Answer and Explanation:

The method that can be used to solve all quadratic equations is the quadratic formula. The quadratic formula states that if ax2 + bx + c = 0, then x = − b ± b 2 − 4 a c 2 a .

The graph of a quadratic function is a parabola. The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0, the zeros of a quadratic function occur where f(x) = 0, or at the x-values that make a x 2 + b x + c = 0 a true equation.

Quadratic functions can have one, two, or zero zeros. Zeros are also called the roots of quadratic functions, and they refer to the points where the function intersects the X-axis. The standard form of a quadratic function is ax² + bx + c = 0.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) .

The general form of a quadratic function is f(x)=ax2+bx+c where a, b, and c are real numbers and a≠0. The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a).

One shortcut is to factor the equation. Then set each factor equal to zero. Example; x²+8x+12=0 becomes (x+2)(x+6)=0. Then we know that either x+2=0 or x+6=0.

Step 1: Using inverse operations, move all terms to one side of your equal sign. Step 2: Simplify your equation, and move terms around so that your equation is in the standard form of a quadratic function. Step 3: Now that your equation is in standard form, you can determine the values for a, b, and c.