Chapter II Flashcards
Analyze the graph of the quadratic function.
The standard form of a quadratic function is f(x) = ax^2 + bx + c. What possible values can a and c have for the given quadratic function? Explain your reasoning.
The a-value must be positive because the graph is concave up.
The c-value must be negative because the y-intercept is negative.
Analyze the graph of the quadratic function.
The vertex form of a quadratic function is f(x) = a(x - h)^2 + k. What possible values can a, h, and k have for the given quadratic function? Explain your reasoning.
The a-value must be positive because the graph is concave up. The h-value must be positive because the x-coordinate of the vertex is positive. The k-value must be negative because the y-coordinate of the vertex is negative.
Analyze the graph of the quadratic function.
The factored form of a quadratic function is f(x) = a(x - r_1)(x - r_2). What possible values can a, r_1, and r_2 have? Explain your reasoning.
The a-value must be positive because the graph is concave up. One of the r-values must be negative and the other must be positive because the graph crosses both the negative x-axis and the positive x-axis.
