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# Give the similarities and differences of linear and quadratic function in terms of equation

What is the difference between linear and quadratic functions?

A linear function is one of the form y = mx + c. For each input of x, you get one output for y. The graph of these functions is a single straight line.

A quadratic function is one of the form y = ax2 + bx + c. For each output for y, there can be up to two associated input values of x. The graph of these functions is a parabola – a smooth, approximately u-shaped or n-shaped, curve.

Linear equations are equations of the first degree, meaning that the unknown variable appears with an exponent of 1.

They can always be brought to the form ax + b = 0 where a, b are constants and a ≠ 0.

They have one root (solution) which is x = -b/a.

The graph of their underlying function f(x) = ax + b is a straight line, hence their name.

Quadratic equations are equations of the second degree, meaning that the unknown variable appears with an exponent of 2.

They can always be brought to the form ax² + bx + c = 0 where a, b, c are constants and a ≠ 0.

The constants a, b and c form a quantity D = b² - 4ac, aptly called the Determinant, which determines whether the equation has any real roots.

(This results from the fact that the solution contains the square root of D, which isn’t a ‘real’ number for D < 0.)

If D >= 0, quadratic equations have two real roots (merged into one for D = 0), which can be calculated by the formula:

x₁‚ ₂ = (-b ±√D)/2a

The graph of their underlying function f(x) = ax² + bx + c is a parabola whose arms tend to f(x) = +∞ for a > 0 and to f(x) = -∞ for a < 0.

They take their name (quadratic) from the fact that we call the second power ‘the square’ (Latin: quadratus).

A linear equation in two variables doesn't involve any power higher than one for either variable. It has the general form Ax + By + C = 0, where A, B and C are constants. ... A quadratic equation on the other hand, involves one of the variables raised to the second power.

Explanation:

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A linear equation in two variables doesn't involve any power higher than one for either variable. ... A quadratic equation, on the other hand, involves one of the variables raised to the second power. It has the general form y = ax2 + bx + c.

1. In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as. where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no. term.

2. The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex.

3. A linear equation in two variables doesn't involve any power higher than one for either variable. ... A quadratic equation, on the other hand, involves one of the variables raised to the second power. It has the general form y = ax2 + bx + c.

4. The graph of a quadratic function is a parabola. 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.

5. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

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