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What is the vertex and axis of symmetry of x 4)(x-3)?
To find the vertex and axis of symmetry of the polynomial ( f(x) = (x - 4)(x - 3) ), we first expand it to get ( f(x) = x^2 - 7x + 12 ). The vertex form of a quadratic function ( ax^2 + bx + c ) has its vertex at ( x = -\frac{b}{2a} ). Here, ( a = 1 ) and ( b = -7 ), so the x-coordinate of the vertex is ( x = \frac{7}{2} = 3.5 ). The axis of symmetry is the vertical line ( x = 3.5 ). The vertex itself can be found by substituting ( x = 3.5 ) back into the equation, yielding the vertex as ( (3.5, f(3.5)) ).
Do quadratic functions have the same equations vertex and axis of symmetry?
No, quadratic functions do not have the same equations for the vertex and the axis of symmetry. The vertex of a quadratic function in the standard form ( f(x) = ax^2 + bx + c ) can be found using the formula ( x = -\frac{b}{2a} ), giving the x-coordinate of the vertex. The axis of symmetry is the vertical line that passes through the vertex, which also has the equation ( x = -\frac{b}{2a} ). While they share the same x-coordinate, the vertex represents a point, while the axis of symmetry is a line.
What does the x and y axis on a coordinate plane look like?
the y-axis is vertical, and the x- axis is horizontal
A figure has a vertex at (-1 -3). If the figure has line symmetry about the y-axis what are the coordinates of another vertex of the figure?
If a figure has line symmetry about the y-axis, then for every point (x, y) on the figure, there is a corresponding point (-x, y). Given that one vertex is at (-1, -3), its symmetric counterpart across the y-axis would be at (1, -3). Thus, the coordinates of another vertex of the figure are (1, -3).
What connection exists between the coordinates of the vertex and the equation of the axis of symmetry?
The coordinates of the vertex of a parabola, given by the equation ( y = ax^2 + bx + c ), are found at the point ((h, k)), where (h = -\frac{b}{2a}). The axis of symmetry of the parabola is a vertical line that passes through the vertex, represented by the equation ( x = h ). Thus, the x-coordinate of the vertex directly determines the equation of the axis of symmetry.
What is the vertex and axis of symmetry of x 4)(x-3)?
To find the vertex and axis of symmetry of the polynomial ( f(x) = (x - 4)(x - 3) ), we first expand it to get ( f(x) = x^2 - 7x + 12 ). The vertex form of a quadratic function ( ax^2 + bx + c ) has its vertex at ( x = -\frac{b}{2a} ). Here, ( a = 1 ) and ( b = -7 ), so the x-coordinate of the vertex is ( x = \frac{7}{2} = 3.5 ). The axis of symmetry is the vertical line ( x = 3.5 ). The vertex itself can be found by substituting ( x = 3.5 ) back into the equation, yielding the vertex as ( (3.5, f(3.5)) ).
Do quadratic functions have the same equations vertex and axis of symmetry?
No, quadratic functions do not have the same equations for the vertex and the axis of symmetry. The vertex of a quadratic function in the standard form ( f(x) = ax^2 + bx + c ) can be found using the formula ( x = -\frac{b}{2a} ), giving the x-coordinate of the vertex. The axis of symmetry is the vertical line that passes through the vertex, which also has the equation ( x = -\frac{b}{2a} ). While they share the same x-coordinate, the vertex represents a point, while the axis of symmetry is a line.
What does the graph of x minus x squared look like?
the x-axis... obviously! the x-axis... obviously!
What does the x and y axis on a coordinate plane look like?
the y-axis is vertical, and the x- axis is horizontal
Do all functions of the form y equals ax2 have the same vertex and axis of symmetry?
axis of symmetry is x=0 Vertex is (0,0) So the answer is : YES
Find the vertex and equation of the directri for y2 equals -32x?
y2 = 32x y = ±√32x the vertex is (0, 0) and the axis of symmetry is x-axis or y = 0
What is the axis of symmetry for the parabola with vertex (-2 -4) and directrix y 1?
The axis of symmetry is x = -2.
What are the coordinates of another vertex of the figure A figure has a vertex at (-1 -3). If the figure has line symmetry about the x-axis.?
It is (-1, 3).
A figure has a vertex at (-1 -3). If the figure has line symmetry about the y-axis what are the coordinates of another vertex of the figure?
If a figure has line symmetry about the y-axis, then for every point (x, y) on the figure, there is a corresponding point (-x, y). Given that one vertex is at (-1, -3), its symmetric counterpart across the y-axis would be at (1, -3). Thus, the coordinates of another vertex of the figure are (1, -3).
What connection exists between the coordinates of the vertex and the equation of the axis of symmetry?
The coordinates of the vertex of a parabola, given by the equation ( y = ax^2 + bx + c ), are found at the point ((h, k)), where (h = -\frac{b}{2a}). The axis of symmetry of the parabola is a vertical line that passes through the vertex, represented by the equation ( x = h ). Thus, the x-coordinate of the vertex directly determines the equation of the axis of symmetry.
A figure has a vertex at -1 -3 if the figure has line of symmetry about the x-axis what are the coordinates of another vertex of the figure?
2
What would a graph look like if the equation was x equals 3?
It would look like a straight vertical line, i.e. parallel to the y-axis, passing through the point on the x-axis where x=3.
