sketch the graph of quadratic function. identify vertex and x intercepts

f(x)(x-3)squared-1

To sketch the graph of a quadratic function, we can follow a few steps:

Step 1: Identify the coefficients of the quadratic function. In this case, the quadratic function is given as f(x) = (x - 3)^2 - 1. We can see that the coefficient of the x^2 term is 1 (since it is not explicitly mentioned), the coefficient of the x term is 0 (since there is no x term present), and the constant term is -1.

Step 2: Find the vertex of the parabola. The vertex of a quadratic function in the form f(x) = a(x - h)^2 + k is given by (h, k). In our case, the quadratic function is in vertex form, and we can identify the vertex as (3, -1). The x-value of the vertex is opposite the sign and value inside the parentheses, while the y-value is the constant term outside the parentheses.

Step 3: Calculate the x-intercepts. x-intercepts are the points where the graph crosses the x-axis, meaning the y-coordinate is zero. To find the x-intercepts, set the quadratic function equal to zero and solve for x. In this case, we have (x - 3)^2 - 1 = 0. Expanding and rearranging, we get (x^2 - 6x + 9) - 1 = 0, which simplifies to x^2 - 6x + 8 = 0. We can factor this quadratic equation as (x - 2)(x - 4) = 0. Setting each factor equal to zero, we find x = 2 and x = 4 as the x-intercepts.

Step 4: Plot the vertex and x-intercepts on a graph. The vertex is at (3, -1), and the x-intercepts are at x = 2 and x = 4. Now, connect these points smoothly to form a parabolic curve.

Here is the graph of the quadratic function f(x) = (x - 3)^2 - 1:

^
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7 | +
| +
2 | +
| +
-3|_____________________
-1 2 3 4 5 6