In Exercises 17-34, write the quadratic function in standard form and sketch its graph. Identify

step 1 We need to find the following equation and write it in standard form. Then we need to identify t

In Exercises 17-34, write the quadratic function in standard...

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Key Concepts

X-intercepts

The x-intercepts are the points where the quadratic function crosses the x-axis (where f(x) = 0). These intercepts correspond to the roots or solutions of the quadratic equation and can be found using methods such as factoring, completing the square, or applying the quadratic formula.

Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two symmetric halves. Its equation is x = h, where h is the x-coordinate of the vertex.

Vertex

The vertex of a parabola is the point where it attains its maximum or minimum value, depending on whether it opens downward or upward, respectively. It directly indicates the turning point of the function.

Standard Form

The standard form, also called vertex form, of a quadratic function is written as f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. This form simplifies identifying key features such as the vertex and axis of symmetry.

Quadratic Function

A quadratic function is a second-degree polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants with a ? 0. It represents a parabolic graph that opens upward if a is positive and downward if a is negative.

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