Quadratic Equations on the Plane
<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-quadratic-equations-on-the-plane" target="_blank">Quadratic Equations on the Plane Exercise</a></span></p>
<p><strong>Note:</strong> around 5:30 into the video, Greg discusses the concept of a y-intercept in the video. However, the explanation on what the y-intercept is incorrect. If we look at the definition of the y-intercept, it's when the curve touches the y-axis. Recall that for a line, we do this by setting $x = 0$ in the equation. It's the same thing for a quadratic. In other words, </p>
<p>- if $y = (x + a)^2 + b$, the y-intercept is <strong>not</strong> $b$ as shown in the video<br />
- if the quadratic is written in the form $y = ax^2 + bx + c$, the y-intercept <strong>is</strong> $c$. You can confirm this by setting $x = 0$ in the previous equation.</p><p>The diagram below illustrates <span style="color:#27ae60;">Quadratic Equations on the Plane</span>. They can have $2$, $1$, or $0$ $x$-intercepts. Also, if there is a negative sign in front of the $x^2$ term, like in $y=-x^2 -2$, the parabola flips upside down.</p>
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