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How to Find the Y Intercept in a Quadratic Equation
Quadratic equations are mathematical functions where one of the x variables is squared, or taken to the second power like this: x2. When these functions are graphed, they create a parabola which looks like a curved “U” shape on the graph. This is why a quadratic equation is sometimes called a parabola equation.
Two important values concerning these mathematical functions are the x-intercept and the y-intercept. The x-intercept indicates where the parabola graph of that function crosses the x axis. There can be one or two x intercepts for a single quadratic equations.
The y-intercept indicates where the parabola crosses the y axis. There is only one y intercept for each quadratic equation.
What Is the y Intercept of a Quadratic Function?
The y-intercept is where the parabola of a function crosses (or intercepts) the y axis. Another way to define the y-intercept is the value of y when x is equal to zero.
Because the y intercept is a point on a graph, you’ll usually write it in point/coordinate form. For example, let’s say your y value of the y intercept is 6.5. You would write the y intercept as (0, 6.5).
Different Forms of Quadratic Equations
Quadratic equations come in three general forms. These are the standard form, vertex form and factored form.
Standard form looks like this:
y = ax2 + bx + c where a, b and c are known constants and x and y are variables.
Vertex form looks like this:
y = a(x + b)2 + c where a, b and c are known constants and x and y are variables.
Factored form looks like this:
y = a(x + r1)(x + r2) where a is a known constant, r1 and r2 are “roots” of the equation (x intercepts), and x and y are variables.
Each of the forms looks drastically different, but the method for finding the y intercept of a quadratic equation is the same despite the various forms.
How to Find the Y Intercept of a Quadratic in Standard Form
Standard form is perhaps the most common and the easiest to understand. Simply plug zero (0) in as the value of x in the standard quadratic equation and solve. Here’s an example.
Let’s say your function is y = 5×2 + 11x + 72. Assign “0” as your x value and solve.
y = 5(0)2 + 11(0) + 72 = 72
You would then write the answer in the coordinate form of (0, 72).
How to Find the Y Intercept of a Quadratic in Vertex Form
As with standard form, simply plug “0” in as the value of x and solve. Here’s an example.
Let’s say your function is y = 134(x + 56)2 – 47. Assign “0” as your x value and solve.
y = 134(0 + 56)2 – 47 = 134(0)2 – 47 = -47
You would then write the answer in the coordinate form of (0, -47).
How to Find the Y Intercept of a Quadratic in Factored Form
Lastly, you have factored form. Again, you simply plug “0” in as the value of x and solve. Here’s an example.
Let’s say your function is y = 7(x – 8)(x + 2). Assign “0” as your x value and solve.
y = 7(0-8)(0+2) = 7(-8)(2) = -112
You would then write the answer in the coordinate form of (0, -112).
A Quick Trick
With both standard and vertex form, you may have noticed that the y-intercept value is equal to the value of the c constant in the equation itself. That is going to be true with every parabola/quadratic equation you encounter in those forms.
Simply look for the c constant and that is going to be your y-intercept. You can double check by using the x value of zero method.
PDF Chapter 3 Quadratic Functions – Section 3.2 Investigating Quadratic Functions in Standard Form. Section 3.3 Completing the Square. Chapter 3 Review. Section 3.1 Page 157 Question 1. a) The graph of f(x) = 7×2 will open upward and be narrower than the graph of f(x) = x2, since a > 1. The parabola will have a minimum value and a…So, to find the y-intercept, plug zero in for x and solve the equation. f(x) = (0-8)(x+3) f(x) =(-8)(3) f(x) = -24 y intercept is -24 the ordered pair is (0, -24). A rectangular ballroom is being carpeted. The room measures 32 feet by 24 feet. If the carpet costs $3.60 per square foot, then what is teh cost of th … e…Start studying Quadratic Functions: Factored Form. Learn vocabulary, terms and more with flashcards, games and other study tools. What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)?
What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)? – are given by the quadratic formula. The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values. The LCM is the smallest positive number that all of the numbers divide into evenly. 1. List the prime factors of each number.y-intercept of a Quadratic Function or Parabola. Examples of How to Find the x and y-intercepts of a Line, Parabola, and Circle. Example 1: From the graph, describe the x and y-intercepts using point notation. The graph crosses the x-axis at x= 1 and x= 3, therefore, we can write the x-intercepts as…
Quadratic Functions: Factored Form Flashcards | Quizlet – Finding x-intercepts and y-intercepts. The intercepts of a graph are points at which the graph crosses the axes. We can confirm that our results make sense by observing a graph of the equation as in Figure 10. Notice that the graph crosses the axes where we predicted it would.The quadratic equation is used to find the intercepts of a function (F(x)=x^(2*n), n being an even number) along its primary axis (typically the x axis). The y-intercept is the product of the x-intercepts multipied together. Example: x²-10x-24 = (x+2)(x-12) +2 and -12 are the constants.Graph equations, system of equations or quadratic equations with our free step-by-step algebra calculator. Vocabulary: The standard format of a quadratic equation is y = ax2 + bx + c; a, b, c are constants; x is the independent variable, and y is the dependent variable.
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