Algebra Quadratic Equations

When a quadratic equation has one solution, there will be one x-intercept; when there are two solutions, there will be two x-intercepts and when the equation has no solution, the graph will have no x-intercepts",is there another way of determining this?

  1. 👍
  2. 👎
  3. 👁
  1. The statement is true, if you are talking about a graph of ax^2 + bc + c vs x, and if the equation you are trying to solve is
    ax^2 + bx + c = 0

    Another way of predicting the number of solutions is calculatin b^2 - 4ac. If it is zero there is one solution. If it is postive there are two. If it is negative there are none.

    1. 👍
    2. 👎
  2. You are referring to the discriminant, which is part of the quadratic formula in the RADICAND section.

    Here is how the discriminant works:

    Given a quadratic equation in the forn
    ax^2 + bx + c = 0, plug the coefficients into the expression
    b^2 - 4ac to see what happens. The expression b^2 - 4ac is called the DISCRIMINANT and it is located in the RADICAND section of the quadratic formula.

    1-If you get a positive number, the quadratic will have 2 unique solutions.

    2-If you get ZERO, the quadratic will have exactly ONE solution, a double root.

    3-If you get a negative number, the quadratic will have NO real solutions, just TWO imaginary ones. In other words, solutions will have the letter i, which is short for "imaginary number."

    Is this clear?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus

    Write an equation for the quadratic graphed below x-intercepts: (-2,0) and (1,0). y-intercept: (0,-2)

  2. math

    Write an equation for the quadratic with x-intercepts (-1,0) and (3,0); and y-intercept (0,-2)!!! Please help ASAP!!! :(

  3. math

    Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve? A. One side of the

  4. math help how do i do this

    Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring. −b b^2 − 4ac 2a Use the part of the quadratic formula that you chose above and find its value, given the following

  1. Math

    Lesson 8: Systems of Linear and Quadratic Equations Check my work 1. Solve the system of equations. y = 2x^2 - 3 y = 3x - 1 a. no solution b. (-1/2, 5), (2, -5/2) c. (-1/2, -5/2), (2,5)*** d. (1/2, 5/2), (2, 5) 2.how many real

  2. math

    This is for the pretest. What is the solution to the system of equations pictured below? A.(-3,5) B.(-3,-2) C(3,4) D.(1,2) E(6,-2) When writing in slope intercept form what does the 'm" Represent? What is the 'b'? A. M is the x

  3. algerba

    What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has? What are the solutions to the quadratic equation 4(x +

  4. Math

    Write an equation to represent a rational function with the following conditions: - reciprocal of a quadratic function - asymptotes with the equations x = -5, x= 4/3, and y = 0 - y < 0 whenever x < -5 - y-intercept of 1.5

  1. linear systems

    The statement that is false is A. A system of quadratic-quadratic equations can have exactly one solution. B. A system of quadratic-quadratic equations has no solutions if the graphs do not intersect. C. It is impossible for a

  2. Mathematics

    For question 1 & 2, find the x- and y-intercept of the line. 1. -10x + 5y = 40 A. x-intercept is 5; y-intercept is -10 B. x-intercept is 8; y-intercept is -4 C. x-intercept is -10; y-intercept is 5 D. x-intercept is -4;

  3. algebra

    Q: when graphing the equation y = 4/3x + 2, the y intercept is? A: (0,2) Q: Determine whether - 3.5 is a solution of the inequality. x greater than or equal to 6 A: No Q:identify the y intercept of y = x + 8 A: (0,8) Q:solve using

  4. Math

    Determine an equation in simplified form, for the family of quadratic functions with zeros -1 -+ √5 and 2 -+ √2 B) determine an equation for the member of the family whose graph has a y intercept of -32

You can view more similar questions or ask a new question.