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Recall that the graph of a linear equation in two variables is a line. The equation

y = ax^2 + bx + c, where a, b, and c are real numbers and a is different than 0 represents a quadratic function. Its graph is a parabola, a smooth and symmetric U-shape.

1. The axis of symmetry is the line that divides the parabola into two matching parts.

Its equation is x = -b/2a

2. The highest or lowest point on a parabola is called the vertex (also called a turning point). Its x-coordinate is the value of -b/2a.

If a > 0, the parabola opens upward, and the vertex is the lowest point on the parabola. The y-coordinate of the vertex is the minimum value of the function.

If a < 0, the parabola opens downward, and the vertex is the highest point on the parabola. The y-coordinate of the vertex is the maximum value of the function.

3. The x-intercepts of the graph of y = ax^2 + bx + c are the real solutions to ax^2 + bx + c = 0.

The nature of the roots of a quadratic function can be determined by looking at its graph.

If you see that there are two x-intercepts on the graph of the equation, then the equation has two real roots.

If you see that there is one x-intercept on the graph of the equation, then the equation has one real roots.

If you see that the graph of the equation never crosses the x-axis, then the equation has no real roots.

The roots can be used further to determine the factors of the equation, as

(x - r1)(x -r2) = 0

Q: How do you solve quadratics using graphing?

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Evariste Galois worked on quadratics when he was a teenager. He was able to establish the means to solve quadratics using radicals and laid the ground work for what became Galois theory. Unfortunately, he died when he was only 20 years old during a duel.

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A graphing calculator is used to plot graphs and solve equations. Most graphing calculators are programmable so one can create customized programs.

Which of the following is a disadvantage to using equations?

Graphing is not necessarily easier than elimination or substitution. If you are good at drawing graphs, and do not like algebra, then graphing is easier. However, elimination and substitution are much faster, and graphing can often get awkward when working with more complicated formulae.

Related questions

Awnser = Start paying attention in class.

1. Quadratics should always contain a set of numbers inconjuction with letters (x usually). 2. Quadratics are always in the form ax2 + bx + c. Where a,b and c are constants and x is a variable. 'a' must always equal '0'. 3. The total equation must never equal '0'. 4. To solve quadratics, you DO NOT factorise. 5. To solve quadratics, use the formula x=a, therefore, b=c. 6. The word 'quadratics' literally means four. This in term means that there are four ways you can solve for the answer of the equation.

Evariste Galois worked on quadratics when he was a teenager. He was able to establish the means to solve quadratics using radicals and laid the ground work for what became Galois theory. Unfortunately, he died when he was only 20 years old during a duel.

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josh hutcherson

This looks like a question from a Virtual School course - please ask you teacher for help and use the examples in the lesson.

elimination, substitution and graphing

A graphing calculator is used to plot graphs and solve equations. Most graphing calculators are programmable so one can create customized programs.

yes

The Babylonians solve quadratics in radicals about 2500 B.C.E. It was Euclid, ca. 300 B.C.E. who demonstrates a geometrical construction for solving a quadratic. however, he does not solve it.

Set it equal to 0 and subtract x and solve for y

You cannot solve x plus y since that is an expression, not an equation (nor inequality).