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What are the solutions for x when y equals 0 in the quadratic function y equals x2 plus x?
y = x2 + x = 0 x (X + 1) = 0 x = 0 is one solution x = -1 is the other
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
How do you translate Quadratic equation?
Translate to what? I assume you need help interpreting it. The quadratic equation is used to solve the quadratic polynomial, ax2 + bx + c = 0, where a, b, and c can be any number. For example, if you need to solve the equation x2 = 5 + 2x, you first convert it into the standard form mentioned above: x2 - 2x - 5 = 0. Now find the coefficients, a, b, and c. In this case, a = 1, b = -2, c = -5. Finally, you replace these coefficients in the quadratic equation. The "plus-minus" sign simply means that the quadratic equation is a shortcut for two equations - one in which you add, the other in which you subtract, the terms at the top. The solutions given by the quadratic equation are values of "x" that satisfy the equation.
How to compute the minimum and maximum function values of a quadratic function?
Suppose you have a quadratic function of the form y = ax2 + bx + c where a, b and c are real numbers and a is non-zero. [If a = 0 it is not a quadratic!] The turning point for this function may be obtained by differentiating the equation with respect to x, or by completing the squares. However you get there, the turning point is the solution to 2ax + b = 0 or x = -b/2a Now, if a > 0 then the quadratic has a minimum at x = -b/2a and it has no maximum because y tends to +∞ as x tends to ±∞ . if a < 0 then the quadratic has a maximum at x = -b/2a and it has no minimum because y tends to -∞ as x tends to ±∞. You evaluate the value of y at this point. y = a(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = -b2/4a + c = -(b2 - 4ac)/4a In either case, if the domain of the function is bounded on both sides, then the missing extremum will be at one or the other bound - whichever is further away from (-b/2a).
What are 3 other names for solutions of a quadratic equation?
Roots, zeroes, and x values are 3 other names for solutions of a quadratic equation.
What are other names for solutions of a quadratic?
They are the roots or zeros. They are also the x-intercepts if they are real numbers.
How many solution will there be if the quadratic equation does not touch or cross the x-axis?
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
What is the average of the two soultions for the quadratic equation?
Replace the discriminant (the root) in the quadratic formula with zero - that will give you the average. In other words: (average of solutions) = -b/2a.
What is a zero of a quadratic function?
The "zero" or "root" of such a function - or of any other function - is the answer to the question: "What value must the variable 'x' have, to let the function have a value of zero?" Or any other variable, depending how the function is defined.
Other names for input of a function?
other names for the input of a function are: 1. x 2. domain
What are the solutions for x when y equals 0 in the quadratic function y equals x2 plus x?
y = x2 + x = 0 x (X + 1) = 0 x = 0 is one solution x = -1 is the other
What is the quadratic formula used for?
The quadratic formula is used all the time to solve quadratic equations, often when the factors are fractions or decimals but sometimes as the first choice of solving method. The quadratic formula is sometimes faster than completing the square or any other factoring methods. Quadratic formula find: -x-intercept -where the parabola cross the x-axis -roots -solutions
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
What does it mean if the quadratic equation has no solution?
Generally, when we say a quadratic equation has no solutions, it means that the graph does not cross the x-axis at all.In other words, it means that there are no values for x when y equals 0 (because the line y=0 IS the x-axis.)Hope that helps.Jamz159
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
In the case of a quadratic function what is the number of x and y intercepts the function may have?
The greatest possible number of intercepts is: 2 of one axis and 1 of the other axis.The smallest possible number of intercepts is: One of each axis.
