# Week 8 – Solving a quadratic equation graphically

This week in pre-calc, we learned how to find the key points in a quadratic equation so we can use them to graph a quadratic equation.

The first step in solving a quadratic equation (ax + bx + c = 0) for graphing is when you see your equation, you can tell right away if the parabola is opening up or opening down. If the co-efficient on the first term (ax) is a positive, it will always open up and if it is negative, it’ll open down.

You can figure out wether the vertex is at its minimum point or maximum point. If its positive, the vertex will be at its minimum and if its negative, the vertex will be at its maximum point.

The next thing you’ll be able to tell from the quadratic equation is the y-intercept. You can tell by finding the constant term. If there is no constant term, the y-intercept is 0. The y-intercept is always crossed when x is always 0.

One way to find the x-intercepts is to factor the equation. When you do this you’ll have something like (x+a)(x-a) = 0

When you have this, the value of both x’s needs to be equal to 0 so in the first one, x would be equal to -a and for the second, x is equal to +a. So the value of x is always the opposite of the given number. When the x-intercept is crossed, y will always be at 0.