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15. Which of the following is the equation of the given graph below?
A. y=(-1/2)x2+5
B. y=-3(x-3)2+5
C. y=-3x2+4
D. y=(-x2/2)+4
16. Given the quadratic function y=3x2-12x + 1, how can the axis of symmetry be described?
A. The axis of symmetry will pass either through the x axis or the y axis. B. The axis of symmetry will intersect the both the x and the y axes at 2. C. The axis of symmetry will pass through the x axis at x = 2.
D. The axis of symmetry will pass through the y axis at y = 2
15. Which of the following is the equation of the given graph below?
A. y=(-1/2)x2+5
B. y=-3(x-3)2+5
C. y=-3x2+4
D. y=(-x2/2)+4
16. Given the quadratic function y=3x2-12x + 1, how can the axis of symmetry be described?
A. The axis of symmetry will pass either through the x axis or the y axis. B. The axis of symmetry will intersect the both the x and the y axes at 2. C. The axis of symmetry will pass through the x axis at x = 2.
D. The axis of symmetry will pass through the y axis at y = 2
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Answer:
15. To determine the equation of the given graph, we need to analyze the key features of the graph. By comparing the given options with the graph, we can see that option B, y=-3(x-3)2+5, matches the graph. This equation represents a quadratic function that has been shifted 3 units to the right and 5 units up from the standard form of a quadratic equation.
16. The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two equal halves. It is always in the form x = a, where 'a' is the x-coordinate of the vertex.
In the given quadratic function y=3x2-12x + 1, we can find the axis of symmetry by using the formula x = -b/(2a), where 'a' and 'b' are the coefficients of the quadratic equation.
In this case, a = 3 and b = -12. Plugging these values into the formula, we get x = -(-12)/(2*3) = 2.
Therefore, the axis of symmetry can be described as passing through the x-axis at x = 2. Option C, "The axis of symmetry will pass through the x-axis at x = 2," is the correct answer.