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The vertex of this parabola is at 3 1 When the y-value is 0 the x-value is 4 What is the coefficient of the squared term in the parabolas equation?
To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Given the vertex at (3, 1), the equation starts as (y = a(x - 3)^2 + 1). Since the parabola passes through the point (4, 0), we can substitute these values into the equation: (0 = a(4 - 3)^2 + 1), resulting in (0 = a(1) + 1). Solving for (a), we find (a = -1). Thus, the coefficient of the squared term is (-1).
What do you notice the shape of the graph x of the quadratic function yax2?
The shape of the graph of the quadratic function ( y = ax^2 ) is a parabola. If the coefficient ( a ) is positive, the parabola opens upwards, while if ( a ) is negative, it opens downwards. The vertex of the parabola is its highest or lowest point, depending on the direction it opens. The axis of symmetry is the vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.
When does a parabola open upward?
A parabola opens upward when its leading coefficient (the coefficient of the (x^2) term in the quadratic equation (y = ax^2 + bx + c)) is positive. This means that as you move away from the vertex of the parabola in both the left and right directions, the values of (y) increase. Consequently, the vertex serves as the minimum point of the parabola.
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
Is the y intercept a vertical line through the vertex of a parabola?
No.
What is an equation of the parabola in vertex form that passes through (13 8) and has vertex (3 2).?
please help
The vertex of this parabola is at 3 1 When the y-value is 0 the x-value is 4 What is the coefficient of the squared term in the parabolas equation?
To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Given the vertex at (3, 1), the equation starts as (y = a(x - 3)^2 + 1). Since the parabola passes through the point (4, 0), we can substitute these values into the equation: (0 = a(4 - 3)^2 + 1), resulting in (0 = a(1) + 1). Solving for (a), we find (a = -1). Thus, the coefficient of the squared term is (-1).
What do you notice the shape of the graph x of the quadratic function yax2?
The shape of the graph of the quadratic function ( y = ax^2 ) is a parabola. If the coefficient ( a ) is positive, the parabola opens upwards, while if ( a ) is negative, it opens downwards. The vertex of the parabola is its highest or lowest point, depending on the direction it opens. The axis of symmetry is the vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5 What is the coefficient of the squared term in the parabola's equation?
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
The vertex of this parabola is at 5 5 When the x-value is 6 the y-value is -1 What is the coefficient of the squared expression in the parabola's equation?
The vertex of this parabola is at 5 5 When the x-value is 6 the y-value is -1. The coefficient of the squared expression in the parabola's equation is -6.
When does a parabola open upward?
A parabola opens upward when its leading coefficient (the coefficient of the (x^2) term in the quadratic equation (y = ax^2 + bx + c)) is positive. This means that as you move away from the vertex of the parabola in both the left and right directions, the values of (y) increase. Consequently, the vertex serves as the minimum point of the parabola.
The vertex of this parabola is at (2, -4) When the y-value is -3, the x-value is -3 What is the coefficient of the squared term in the parabola's equation?
-5
The vertex of this parabola is at 4 -3 When the x-value is 5 the y-value is -6 What is the coefficient of the squared expression in the parabola's equation?
-3
The vertex of this parabola is at (4 -3). When the x-value is 5 the y-value is -6. What is the coefficient of the squared expression in the parabola's equation?
-3
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
The vertex of this parabola is at -3 -1 When the y-value is 0 the x-value is 4 What is the coefficient of the squared term in the parabolas equation?
The vertex of this parabola is at -3 -1 When the y-value is 0 the x-value is 4. The coefficient of the squared term in the parabolas equation is 7
How do you get a parabola with only one x intercept?
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
