Podcast
Questions and Answers
For the quadratic function $f(x) = x^2 - 10$, over what interval is the function increasing?
For the quadratic function $f(x) = x^2 - 10$, over what interval is the function increasing?
- $x > 0$ (correct)
- $x < 0$
- $x < -10$
- $x > -10$
A parabola has a vertex at $(-2, 6)$, opens downward, and has zeros at $x = -5$ and $x = 1$. Over what interval is the function decreasing?
A parabola has a vertex at $(-2, 6)$, opens downward, and has zeros at $x = -5$ and $x = 1$. Over what interval is the function decreasing?
- $x < -2$
- All real numbers
- $-5 < x < 1$
- $x > -2$ (correct)
Which of the following characteristics describes a parabola with a negative "a" value and a vertex in Quadrant II?
Which of the following characteristics describes a parabola with a negative "a" value and a vertex in Quadrant II?
- Opens upwards with vertex in the fourth quadrant
- Opens upwards with vertex in the second quadrant
- Opens downwards with vertex in the fourth quadrant
- Opens downwards with vertex in the second quadrant (correct)
What equation represents the axis of symmetry for a parabola whose graph is symmetric about the vertical line passing through $x = -1$?
What equation represents the axis of symmetry for a parabola whose graph is symmetric about the vertical line passing through $x = -1$?
Given the quadratic function $g(x) = 4x^2 - 16x + 19$, which calculation correctly finds the x-coordinate of the vertex using the formula $x = -b/2a$?
Given the quadratic function $g(x) = 4x^2 - 16x + 19$, which calculation correctly finds the x-coordinate of the vertex using the formula $x = -b/2a$?
A parabola opens upwards and its vertex is at $(2, 3)$. What is the range of this quadratic function?
A parabola opens upwards and its vertex is at $(2, 3)$. What is the range of this quadratic function?
A quadratic function has a domain of all real numbers and a range of $y \le 4$. Which statement must be true about the graph of this function?
A quadratic function has a domain of all real numbers and a range of $y \le 4$. Which statement must be true about the graph of this function?
Andy graphed a quadratic function with a vertex at $(9, -5)$ and two zeros. What is the range of the function?
Andy graphed a quadratic function with a vertex at $(9, -5)$ and two zeros. What is the range of the function?
If a quadratic function has a domain of all real numbers, which statement is true?
If a quadratic function has a domain of all real numbers, which statement is true?
Which of the following quadratic functions will have a range of all real numbers greater than or equal to -3?
Which of the following quadratic functions will have a range of all real numbers greater than or equal to -3?
How does changing the value of 'a' in the quadratic equation $f(x) = ax^2 + bx + c$ affect the parabola's graph?
How does changing the value of 'a' in the quadratic equation $f(x) = ax^2 + bx + c$ affect the parabola's graph?
If a parabola has only one x-intercept, what can be concluded about its vertex?
If a parabola has only one x-intercept, what can be concluded about its vertex?
Given the quadratic function $f(x) = -2(x - 3)^2 + 5$, what is the vertex of the parabola and does it open upwards or downwards?
Given the quadratic function $f(x) = -2(x - 3)^2 + 5$, what is the vertex of the parabola and does it open upwards or downwards?
Which statement accurately explains how the axis of symmetry relates to the vertex of a parabola?
Which statement accurately explains how the axis of symmetry relates to the vertex of a parabola?
A quadratic equation has no real solutions. What does this imply about the graph of the corresponding quadratic function?
A quadratic equation has no real solutions. What does this imply about the graph of the corresponding quadratic function?
In the standard form of a quadratic equation, $ax^2 + bx + c = 0$, what does the 'c' value represent graphically?
In the standard form of a quadratic equation, $ax^2 + bx + c = 0$, what does the 'c' value represent graphically?
How does decreasing the 'b' value (while keeping 'a' positive) affect the location of the vertex in the quadratic equation $f(x)=ax^2+bx+c$?
How does decreasing the 'b' value (while keeping 'a' positive) affect the location of the vertex in the quadratic equation $f(x)=ax^2+bx+c$?
Which of the following statements is true for any quadratic function?
Which of the following statements is true for any quadratic function?
Given a parabola with a vertex at (h, k), under what condition will the range of the function be all real numbers?
Given a parabola with a vertex at (h, k), under what condition will the range of the function be all real numbers?
Flashcards
What is a vertex?
What is a vertex?
The highest or lowest point on a parabola.
Parabola Maximum Value
Parabola Maximum Value
The maximum value of this parabola is 6.
What are zeros of a parabola?
What are zeros of a parabola?
The points where the parabola intersects the x-axis, also known as roots.
What is the y-intercept?
What is the y-intercept?
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What does increasing mean?
What does increasing mean?
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What does decreasing mean?
What does decreasing mean?
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What does positive mean?
What does positive mean?
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What does negative mean?
What does negative mean?
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Negative 'a' Value
Negative 'a' Value
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What is Quadrant II?
What is Quadrant II?
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Positive & Negative Zero
Positive & Negative Zero
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Axis of Symmetry
Axis of Symmetry
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Axis of Symmetry Equation
Axis of Symmetry Equation
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Vertex
Vertex
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Domain of a Quadratic Function
Domain of a Quadratic Function
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Range of a Quadratic Function
Range of a Quadratic Function
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Domain and Range
Domain and Range
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Study Notes
Graphing Quadratic Functions and Identifying Key Attributes
- The table of values can be used to create a graph of f(x) = x² - 10.
- For f(x) = x² - 10, it is increasing when x > 0 and decreasing when x < 0.
- The example parabola has a vertex at (-2, 6).
- The example parabola has a maximum of 6.
- The example parabola has zeros at -5 and 1.
- The example parabola has a y-intercept at (0, 3).
- The example parabola is increasing when x < -2.
- The example parabola is decreasing when x > -2.
- The example parabola is positive when -5 < x < 1.
- The example parabola is negative when x < -5 or x > 1.
- A parabola can be sketched, given attributes
- The example parabola has a negative "a" value, a vertex in quadrant II, and one positive and one negative zero.
- An equation for the axis of symmetry of example parabola is x = -1.
- For g(x) = 4x² - 16x + 19, -b/2a can be used to find the vertex and axis of symmetry equation.
- For g(x) = 4x² - 16x + 19, the axis of symmetry is x = 2 and vertex is (2, 3).
Determining the Domain and Range of Quadratic Functions
- The domain and range of a quadratic function can be determined from its graph.
- For the upward-facing parabola, the domain (D) is all real numbers and range (R) is y ≤ 4.
- Andy graphed a quadratic function with a vertex at (9, -5) and two zeros.
- For Andy's graph, the domain (D) is all real numbers, and range (R) is y ≥ 5.
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