This week in Pre-Calc 11 we finished up our quadratic unit, reviewed for our midterm and started our analyzing quadratic equations unit. Although we haven’t gotten to in depth about this unit yet I am going to focus on the few things we have learned. In this blog post, I am going to show how to analyze a quadratic equation and what the equation can show us without even doing any solving or anything.
First of all, what is a quadratic equation? Compared to a linear equation? A quadratic equation is an equation with a degree of 2, while a linear equation has a degree of 1.
Let’s take this quadratic equation. There are certain things you can already know about this equation without using a graphing calculator or any other thing like that.
Y-intercept: The Y-intercept is where the line (s) touch the y axes. Without doing any graphing I can see that the Y-intercept in this equation is going to be 5. The Y-intercept is always the number in the equation without a variable.
X-Intercept: The X-intercept is where the line crosses the X axes. In this case when we graph it we see there is no X-intercept because the parabola never crosses the X axes.
The coordinates of the vertex: The vertex is the bottom or top part of the parabola. So you can see in this case the coordinates are (2,3) because that is the lowest part of the parabola.
The equation of the axis of symmetry: The axes of symmetry is an invincible lines going right through the middle of the parabola. If you look at the graph you can see, if a line went right through the middle of it down to the X-axes it is going to be x=2.
The domain of the function: As you can see the domain is the restrictions on the X axis. But if you can see X can be anything. The parabola can go on forever. Therefor, XER, because x can be any value and be true.
The range of the function: The range is the restrictions on the Y. As you can see the Y doesn’t go and can’t go lower than 3. So X≥3, because it can’t go down any lower than 3.
Those are a few simple things you can know about your quadratic equation before solving or doing any real work. One thing i’ll add is the x^2 value is + the parabola will be minimum, but if the value is – the parabola will be maximum, meaning it will open-down.
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