5 Questions
Which equation represents the graph of the parabola shown?
B. $f(x) = -3(x-3)^2-1$
What is the equation of the quadratic function with roots at -3 and -7 and a vertex at (-5, 4)?
A. $f(x) = (x+5)^2 - 4$
Which inequality represents the graph of the quadratic inequality shown?
B. $f(x) \leq 2x^2 - 16x + 29$
What is the vertex form of the quadratic function $f(x) = x^2 - 4x - 21$?
A. $f(x) = (x+2)^2 - 17$
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?
A. 2
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.
Test your knowledge of quadratic functions and parabolas with this quiz! Determine the correct equations that represent given graphs and find the equation of a parabola with given roots and a vertex. Challenge yourself and sharpen your skills in quadratic functions!
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