![]() ![]() ![]() (Note: students will likely need to experiment quite a bit to find an equation that satisfies these constraints. The following go through the points $(-4,2)$ and $(1, 2)$: ![]() The following have $x$-intercepts at the origin and $(-4,0)$: The following have a $y$-intercept of $(0,-6)$ : The following have a vertex at $(-2,-5)$ : Asking students for three possible answers is a great extension for students - it gets them thinking about the effects of the different parts of the equation. Let us draw the graph for the quadratic polynomial function f(x) x 2. Then we plot the points from the table and join them by a curve. We’re including three possible answers for each one, to demonstrate the type of variability you might expect to see in a class. To graph a simple polynomial function, we usually make a table of values with some random values of x and the corresponding values of f(x). Note: each of these problems has many possible answers. The $x$-intercepts are $(3,0)$ and $(-1, 0)$, which are most visible in $y_1$ since you can find the roots of the polynomial using the zerofactor property and thus the intercepts correspond to the zeros of each factor. The $y$-intercept is $(0, -3)$, which is visible as the constant in $y_2$ since the other terms are 0 when you plug in $x = 0$. Along with plotting points and linear equations, the graphing tool on Quizizz enables you to work with quadratic equations and exponential functions. The vertex is $(1, -4)$ which is most visible in $y_3$ since the vertex occurs at the point where the squared portion is zero. We can see that the difference between it and $y_2$ is just 4, so that graph is 4 units below the other one. The quadratic formula gives solutions to the quadratic equation ax2+bx+c0 and is written in the form of x (-b (b2 - 4ac)) / (2a) Does any quadratic equation have two solutions There can be 0, 1 or 2 solutions to a quadratic equation. The fourth function produces a different graph. Similarly, if we multiply out the perfect square and combine like terms in the third equation, we also get the second one: In this form, the quadratic equation is written as. For example, two standard form quadratic equations are f (x) x 2 + 2x + 1 and f (x) 9x 2 + 10x -8. (Both of these functions can be extended so that their domains are the complex numbers, and the ranges change as well.) Domain and Range Calculator: Wolfram. In this form, the quadratic equation is written as: f (x) ax 2 + bx + c where a, b, and c are real numbers and a is not equal to zero. The sine function takes the reals (domain) to the closed interval 1,1 1, 1 (range). If we multiply the factors given in the first equation, we’ll get the second equation: For example, the function x2 x 2 takes the reals (domain) to the non-negative reals (range). This is because the first three equations are equivalent, and so all produce the same graph. When you graph these four equations, only two different parabolas are shown. ![]()
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