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Questions and Answers
Which equation represents the graph of the parabola shown?
Which equation represents the graph of the parabola shown?
- D. $f(x) = -2(x-3)^2-1$
- C. $f(x) = -2(x+3)^2-1$
- A. $f(x) = -3(x+3)^2-1$
- B. $f(x) = -3(x-3)^2-1$ (correct)
What is the equation of the quadratic function with roots at -3 and -7 and a vertex at (-5, 4)?
What is the equation of the quadratic function with roots at -3 and -7 and a vertex at (-5, 4)?
- B. $f(x) = (x-5)^2 - 4$
- C. $f(x) = (x+5)^2 + 4$
- D. $f(x) = (x-5)^2 + 4$
- A. $f(x) = (x+5)^2 - 4$ (correct)
Which inequality represents the graph of the quadratic inequality shown?
Which inequality represents the graph of the quadratic inequality shown?
- D. $f(x) < 2x^2 - 16x + 29$
- B. $f(x) \leq 2x^2 - 16x + 29$ (correct)
- A. $f(x) \geq 2x^2 - 16x + 29$
- C. $f(x) > 2x^2 - 16x + 29$
What is the vertex form of the quadratic function $f(x) = x^2 - 4x - 21$?
What is the vertex form of the quadratic function $f(x) = x^2 - 4x - 21$?
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If the quadratic function $f(x) = 2x^2 + 8x + 11$ is changed to the form $f(x) = a(x-h) + k$, what is the value of a?
If the quadratic function $f(x) = 2x^2 + 8x + 11$ is changed to the form $f(x) = a(x-h) + k$, what is the value of a?
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Study Notes
Quadratic Functions and Graphs
- The equation of a parabola can be represented in various forms, including vertex form and standard form.
- The roots of a quadratic function are the x-intercepts of the graph, and can be used to find the equation of the function.
- A quadratic function with roots at -3 and -7 and a vertex at (-5, 4) can be represented by an equation that satisfies these conditions.
Quadratic Inequalities
- The graph of a quadratic inequality can be represented by an inequality, which can be used to identify the region of the graph that satisfies the inequality.
Vertex Form of a Quadratic Function
- The vertex form of a quadratic function f(x) is given by f(x) = a(x-h) + k, where (h, k) is the vertex of the parabola.
- To find the vertex form of a quadratic function, the function must be rewritten in the form f(x) = a(x-h) + k.
Transforming Quadratic Functions
- A quadratic function in the form f(x) = ax^2 + bx + c can be transformed into the form f(x) = a(x-h) + k, where a is a coefficient that affects the shape of the graph.
- The value of a can be found by rewriting the quadratic function in vertex form.
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