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WorksheetsKUIS PERSAMAAN KUADRAT
Total questions: 15
Worksheet time: 4hrs 45mins
Indah is studying quadratic equations for her math exam. What is the standard form of a quadratic equation?
ax² + bx + c = 0
a(x + b) = c
x² + bx + c
ax + b = 0
Identify the coefficients in the equation: 2x² + 3x - 5 = 0.
Coefficients: 2 (for x²), 3 (for x), -5 (constant term)
Coefficients: 2 (for x), 3 (for x²), -5 (constant term)
Coefficients: 1 (for x²), 3 (for x), 5 (constant term)
Coefficients: 2 (for x²), 3 (for x²), -5 (constant term)
What is the quadratic formula used to find the roots of a quadratic equation?
x = (2a ± b) / √(b² - 4ac)
x = (b ± 4ac) / (2√(b²))
x = (b ± √(b² + 4ac)) / (2a)
x = (-b ± √(b² - 4ac)) / (2a)
How many roots can a quadratic equation have?
infinity
4
3
0, 1, or 2
What does the discriminant of a quadratic equation tell us?
The discriminant determines the coefficients of the quadratic equation.
The discriminant indicates the slope of the quadratic function.
The discriminant indicates the nature and number of roots of a quadratic equation.
The discriminant provides the exact values of the roots.
Solve the quadratic equation: x² - 4x + 4 = 0.
x = -2
x = 0
x = 2
x = 4
What is the vertex form of a quadratic equation?
y = ax² + bx + c
y = a(x - h)² + k
y = a(x + h)² - k
y = a(x - h) + k
How do you determine if a quadratic opens upwards or downwards?
The quadratic opens upwards if the coefficient 'b' is positive.
The direction of a quadratic is determined by the sign of the coefficient 'a' in the equation ax² + bx + c.
The direction is determined by the value of 'c' in the equation.
A quadratic always opens downwards regardless of its coefficients.
Find the roots of the equation: x² + 6x + 9 = 0 using factoring.
x = -3
x = 3
x = 0
x = -6
What is the axis of symmetry for the quadratic equation y = x² - 2x + 1?
x = 1
x = -1
x = 2
x = 0
Explain the significance of the vertex in a quadratic graph.
The vertex represents the x-intercept of the graph.
The vertex indicates the slope of the quadratic function.
The vertex is the point where the graph intersects the y-axis.
The vertex is the highest or lowest point of a quadratic graph, indicating the optimal value of the function.
How can you convert a quadratic equation from standard form to vertex form?
y = a(x - h)^2 - k
y = a(x + h)^2 - k
y = a(x - h)^2 + k
y = ax^2 + bx + c
What is the effect of changing the 'a' value in the equation y = ax²?
The 'a' value determines the color of the parabola.
The 'a' value has no effect on the shape of the parabola.
The 'a' value affects the width and direction of the parabola.
Changing 'a' only affects the y-intercept of the graph.
Graph the quadratic function y = -x² + 4. What is its maximum point?
(0, 4)
(-2, 4)
(2, 0)
(0, 0)
What is the relationship between the roots and the factors of a quadratic equation?
The roots are the solutions to the equation, and the factors are the expressions that yield those roots.
The roots are the coefficients of the equation, and the factors are the constants.
The roots are always positive numbers, while the factors are negative.
The roots and factors are unrelated concepts in quadratic equations.
