Graphing Quadratic Functions: Chapter 10 Review

The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex. To graph the function, you can plot the vertex and 4 other points, and then connect the points to form a parabola.

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. It is used to solve quadratic equations by providing the solutions to the equation.

To find the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b / 2a. This will give you the x-coordinate of the vertex, and you can then substitute this value into the function to find the y-coordinate.

<p>The coefficient of the x^2 term determines the direction of the parabola's opening. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards.</p> Signup and view all the answers

<p>The productivity equation P = –0.025t^2 + 3t represents the relationship between the length of a class (in minutes) and the productivity of the students (in %).</p> Signup and view all the answers

<p>To find the productivity, substitute t = 90 into the equation: P = –0.025(90)^2 + 3(90) = 67.5%. The productivity of a class that is 90 minutes long is approximately 67.5%.</p> Signup and view all the answers

<p>The axis of symmetry is the vertical line that passes through the vertex of the parabola, and is given by the equation x = -b / 2a. The axis of symmetry is related to the vertex because it passes through the vertex and is perpendicular to the x-axis.</p> Signup and view all the answers

<p>To find the x-intercepts, set the function equal to zero and solve for x. The x-intercepts represent the points at which the parabola intersects the x-axis, and are the solutions to the equation.</p> Signup and view all the answers