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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)) ).
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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 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 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).
How do you find the vertex using axis of symmetry?
To find the vertex of a parabola using the axis of symmetry, first identify the equation of the parabola in the standard form (y = ax^2 + bx + c). The axis of symmetry can be calculated using the formula (x = -\frac{b}{2a}). Once you have the x-coordinate of the vertex, substitute this value back into the original equation to find the corresponding y-coordinate. The vertex is then given by the point ((-\frac{b}{2a}, f(-\frac{b}{2a}))).
Which letter is key in finding the axis of symmetry?
The key letter in finding the axis of symmetry for a quadratic function in the standard form (y = ax^2 + bx + c) is (b). The axis of symmetry can be calculated using the formula (x = -\frac{b}{2a}), where (a) is the coefficient of (x^2). This formula provides the x-coordinate of the vertex of the parabola, which is also the line of symmetry.
What is the axis of symmetry for the parabola with vertex (-2 -4) and directrix y 1?
The axis of symmetry is x = -2.
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
What is the vertex and the line of symmetry for fx equals 5xsquared?
Vertex = (0,0) Line of symmetry = y axis You should of known that as this function is only X^2
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 are the vertex and the axis of symmetry of the equation y equals 2x² plus 4x - 10?
In the form y = ax² + bx + c the axis of symmetry is given by the line x = -b/2a The axis of symmetry runs through the vertex, and the vertex is given by (-b/2a, -b²/4a + c). For y = 2x² + 4x - 10: → axis of symmetry is x = -4/(2×2) = -4/4 = -1 → vertex = (-1, -4²/(4×2) - 10) = (-1, -16/8 - 10) = (-1, -12)
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).
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
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?
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How do you find the axis of symmetry and vertex of y equals x squared plus 6x plus 10?
By completing the square y = (x+3)2+1 Axis of symmetry and vertex: x = -3 and (-3, 1) Note that the parabola has no x intercepts because the discriminant is less than zero
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).
Which letter is key in finding the axis of symmetry?
The key letter in finding the axis of symmetry for a quadratic function in the standard form (y = ax^2 + bx + c) is (b). The axis of symmetry can be calculated using the formula (x = -\frac{b}{2a}), where (a) is the coefficient of (x^2). This formula provides the x-coordinate of the vertex of the parabola, which is also the line of symmetry.
An equation of a parabola that has x equals 2 as its axis of symmetry is?
How about y = (x - 2)2 = x2 - 4x + 4 ? That is the equation of a parabola whose axis of symmetry is the vertical line, x = 2. Its vertex is located at the point (2, 0).
