To easily graph quadratic functions, I look at a few important parts:
Vertex: First, find the vertex. You can use this formula: [ x = -\frac{b}{2a} ] After that, plug this value back into the equation to find the -value.
Axis of Symmetry: This is a vertical line that goes through the vertex. It looks like this: [ x = -\frac{b}{2a} ] This line helps you to mirror your points when you plot them.
Y-Intercept: You can find the y-intercept by setting to 0. Use this formula: [ f(0) = c ] This comes from the standard form of a quadratic equation: [ y = ax^2 + bx + c ]
X-Intercepts: To find where the graph crosses the x-axis, use the quadratic formula: [ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
Sketching: Now, plot the vertex, the intercepts, and a few extra points. After that, draw a smooth curve that connects everything!
By focusing on these steps, you can make graphing quadratic functions much easier!
To easily graph quadratic functions, I look at a few important parts:
Vertex: First, find the vertex. You can use this formula: [ x = -\frac{b}{2a} ] After that, plug this value back into the equation to find the -value.
Axis of Symmetry: This is a vertical line that goes through the vertex. It looks like this: [ x = -\frac{b}{2a} ] This line helps you to mirror your points when you plot them.
Y-Intercept: You can find the y-intercept by setting to 0. Use this formula: [ f(0) = c ] This comes from the standard form of a quadratic equation: [ y = ax^2 + bx + c ]
X-Intercepts: To find where the graph crosses the x-axis, use the quadratic formula: [ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
Sketching: Now, plot the vertex, the intercepts, and a few extra points. After that, draw a smooth curve that connects everything!
By focusing on these steps, you can make graphing quadratic functions much easier!