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Questions and Answers
For the quadratic function $f(x) = a(x + 1)(x + 5)$, what are the x-intercepts of the graph?
For the quadratic function $f(x) = a(x + 1)(x + 5)$, what are the x-intercepts of the graph?
- (1, 0) and (5, 0)
- (-1, 0) and (-5, 0) (correct)
- (0, 1) and (0, 5)
- (0, -1) and (0, -5)
The equation $kx^2 + 4kx - 1 = k$ always has two real, distinct roots for any real number k.
The equation $kx^2 + 4kx - 1 = k$ always has two real, distinct roots for any real number k.
False (B)
If the y-intercept of the function $f(x) = a(x + 1)(x + 5)$ is (0, -10), what is the value of a?
If the y-intercept of the function $f(x) = a(x + 1)(x + 5)$ is (0, -10), what is the value of a?
2
The axis of symmetry for the quadratic $f(x) = a(x + 1)(x + 5)$ is $x = $ ______.
The axis of symmetry for the quadratic $f(x) = a(x + 1)(x + 5)$ is $x = $ ______.
Match each part of the quadratic function $f(x) = 16 - x^2$ to its description:
Match each part of the quadratic function $f(x) = 16 - x^2$ to its description:
Given $f(x) = log_k(8x - 2x^2)$, for what value of $k$ does the equation $f(x) = 3$ have exactly one solution?
Given $f(x) = log_k(8x - 2x^2)$, for what value of $k$ does the equation $f(x) = 3$ have exactly one solution?
If the graphs of $f(x) = 16 - x^2$ and $g(x) = (x - 4)^2 + k$ intersect only once, then k = 0.
If the graphs of $f(x) = 16 - x^2$ and $g(x) = (x - 4)^2 + k$ intersect only once, then k = 0.
For the rectangle ABCD, where A and B are on the x-axis and C and D are on the graph of $f(x) = 16 - x^2$, if $OA = a$, what is an expression for the area of rectangle ABCD?
For the rectangle ABCD, where A and B are on the x-axis and C and D are on the graph of $f(x) = 16 - x^2$, if $OA = a$, what is an expression for the area of rectangle ABCD?
Flashcards
Quadratic Function
Quadratic Function
A polynomial function of the form f(x) = ax² + bx + c.
X-Intercepts
X-Intercepts
Points where the graph crosses the x-axis (y=0).
Y-Intercept
Y-Intercept
Point where the graph crosses the y-axis (x=0).
Axis of Symmetry
Axis of Symmetry
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Vertex of a Parabola
Vertex of a Parabola
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Reflection in Y-Axis
Reflection in Y-Axis
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Real Distinct Roots
Real Distinct Roots
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Area of Rectangle related to Quadratic
Area of Rectangle related to Quadratic
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Study Notes
Question 26
- A quadratic function is given as f(x) = a(x+1)(x+5) for x ∈ R and a ∈ Z.
- The graph of f has x-intercepts at (p, 0) and (q, 0) and a y-intercept at (0, -10).
- p = -1, q = -5.
- a = 2.
- The equation of the axis of symmetry is x = -3.
- The coordinates of the vertex are (-3, -16).
- A transformation is applied to the graph of f, involving a reflection in the y-axis and a translation.
- The new coordinates of the point Q mapped from P(-2, 6) are (2, 6).
Question 27
- The quadratic equation is kx² + 4kx – 10 = 0
- For real and distinct roots, the discriminant must be positive, Δ > 0.
- Possible values for k are k < -5 or k > 2.
- Given k = 3 the roots are in the form q/√3 where p, q ∈ Z
- The roots are 2 ± √2.
Question 28
- f(x) = logk(8x – 2x²), for 0 < x < 4, and k > 0.
- The equation f(x) = 3 has exactly one solution.
- k = 2
Question 29
- f(x) = x² - kx + 5, for x ∈ R
- g(x) = x + 4, for x ∈ R.
- The range of f(x) is given by f(x) ≥ c. where c is the minimum value of the parabola f(x).
- Given that (gof)(x) ≤ 0 for all real values of x, the set of possible values for k is k ≥ 4.
Question 30
- f(x) = 16 – x²
- x-intercepts are (4, 0) and (-4, 0).
- The area of rectangle ABCD is given by 32a – 2a³.
- The value of a that maximizes the area is 4/√3.
Question 31
- f(x) = 2(x - h₁)² + k₁
- g(x) = (x - h₂)² + k₂
- The vertex of f is (m, -m²) and the vertex of g is (-m, -m).
- 0 < m < 1
- The graphs intersect at exactly one point.
- m = 1/√3.
Question 32
- f(x) = p(x - 1)(x-q).
- y-intercept of f(x) is (0, -3)
- Axis of symmetry is x = 2.
- q = 3.
- p = 1.
- Possible values for k are k = 2, or k = -2/3 ± √13/3
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