When graphing quadratic functions, there are a few important things that every Year 10 student should learn. Let’s go through them step by step!
The vertex is the highest or lowest point of a U-shaped curve called a parabola. If the parabola opens up, the vertex is the lowest point. If it opens down, the vertex is the highest point.
For example, in the quadratic function (y = x^2 - 4x + 3), we can find the vertex using a simple formula:
[ x = -\frac{b}{2a} ]
Here, (a = 1) and (b = -4). When we put those values into the formula, we get (x = 2).
Now, to find the vertex, we put (x = 2) back into the function. We find the vertex at the point ((2, -1)).
The axis of symmetry is a vertical line that goes through the vertex. It splits the parabola into two equal halves that look like mirror images of each other.
In our example, the axis of symmetry is the line (x = 2).
Intercepts tell us where the graph touches the axes:
Y-intercept: To find this, we set (x = 0). For our example, when we do this for (y = x^2 - 4x + 3), we get the Y-intercept at the point ((0, 3)).
X-intercepts: These are where the graph crosses the x-axis, which happens when (y = 0). To find these points, we solve the equation (x^2 - 4x + 3 = 0). This can be factored into ((x - 3)(x - 1) = 0). So, the X-intercepts are at the points ((3, 0)) and ((1, 0)).
By understanding these key features, you can easily draw and understand quadratic functions!
When graphing quadratic functions, there are a few important things that every Year 10 student should learn. Let’s go through them step by step!
The vertex is the highest or lowest point of a U-shaped curve called a parabola. If the parabola opens up, the vertex is the lowest point. If it opens down, the vertex is the highest point.
For example, in the quadratic function (y = x^2 - 4x + 3), we can find the vertex using a simple formula:
[ x = -\frac{b}{2a} ]
Here, (a = 1) and (b = -4). When we put those values into the formula, we get (x = 2).
Now, to find the vertex, we put (x = 2) back into the function. We find the vertex at the point ((2, -1)).
The axis of symmetry is a vertical line that goes through the vertex. It splits the parabola into two equal halves that look like mirror images of each other.
In our example, the axis of symmetry is the line (x = 2).
Intercepts tell us where the graph touches the axes:
Y-intercept: To find this, we set (x = 0). For our example, when we do this for (y = x^2 - 4x + 3), we get the Y-intercept at the point ((0, 3)).
X-intercepts: These are where the graph crosses the x-axis, which happens when (y = 0). To find these points, we solve the equation (x^2 - 4x + 3 = 0). This can be factored into ((x - 3)(x - 1) = 0). So, the X-intercepts are at the points ((3, 0)) and ((1, 0)).
By understanding these key features, you can easily draw and understand quadratic functions!