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Find the Line of Symmetry of a Given Quadratic Parabola Graph
Mathematics
Grade 10 (Junior High School)
Question Content
A quadratic curve is shown in the graph. Write down the equation of the line of symmetry of the curve.
Correct Answer
x = 4
Detailed Solution Steps
1
Step 1: Recall that for a quadratic curve (parabola), the line of symmetry is a vertical line that passes through the vertex (the lowest or highest point) of the parabola.
2
Step 2: Locate the vertex of the given parabola on the graph. The vertex is the lowest point, which has the coordinates (4, -6).
3
Step 3: A vertical line passing through x=4 is the line of symmetry, so its equation is x = 4.
Knowledge Points Involved
1
Line of Symmetry of a Quadratic Parabola
The line of symmetry of a quadratic parabola is a vertical line that divides the parabola into two mirror-image halves. It always passes through the vertex of the parabola. For a quadratic function in the form y=ax²+bx+c, the equation of the line of symmetry is x = -b/(2a); when given a graph, it can be identified by finding the x-coordinate of the vertex.
2
Vertex of a Parabola
The vertex of a parabola is the maximum or minimum point on the curve. For upward-opening parabolas (a>0), it is the minimum point; for downward-opening parabolas (a<0), it is the maximum point. The line of symmetry intersects the parabola exactly at the vertex.
3
Equation of a Vertical Line
Vertical lines on a coordinate plane have equations in the form x = k, where k is a constant representing the x-intercept of the line. These lines have an undefined slope and are parallel to the y-axis.
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