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What is the y coordinate of the vertex of the parabola that is given y equals negative 2 point 5 parenthese x minus 4 parenthese end squared minus 5?
y = -5
By using calculus, the derivative of y = -2.5(x-4)2 - 5 is y' = -5(x-4).
Solving the equation -5(x-4) = 0 gives x = 4 (since the slope of the parabola at the vertex is zero). Plug this back into the equation: y = -2.5(4 - 4) -5 = -5, so the y-coordinate is -5.
The equation of the parabola is given in the vertex form y = a(x - h)2 + k, where (h, k) is the vertex. So the vertex is (4, -5).
What else can I help you with?
In which direction does the parabola that is given by the equation below open..... x equals -2.5 parenthese y - 3 end parenthese squared plus 5?
Left
Where is the vertex coordinate of the parabola y equals 24 -6x -3x squared when plotted on the Cartesian plane?
The vertex coordinate point of the vertex of the parabola y = 24-6x-3x^2 when plotted on the Cartesian plane is at (-1, 27) which can also be found by completing the square.
How do you create an equation for a parabola?
An equation for a parabola always has some type of irregular variable, usually a squared variable or higher.
Parabola y equals one-fourth x squared?
Yes.
What is the coefficient of the squared expression in the parabolas equation?
The coefficient of the squared term in a parabola's equation, typically expressed in the standard form (y = ax^2 + bx + c), is represented by the value (a). This coefficient determines the direction and the width of the parabola: if (a > 0), the parabola opens upwards, and if (a < 0), it opens downwards. The larger the absolute value of (a), the narrower the parabola.
In which direction does the parabola that is given by the equation below open..... x equals -2.5 parenthese y - 3 end parenthese squared plus 5?
Left
What is the parabola?
A parabola is a type of graph that is not linear, and mostly curved. A parabola has the "x squared" sign in it's equation. A parabola is not only curved, but all the symmetrical. The symmetrical point, the middle of the parabola is called the vertex. You can graph this graph with the vertex, x-intercepts and a y-intercept. A parabola that has a positive x squared would be a smile parabola, and the one with the negative x squared would be a frown parabola. Also, there are the parabolas that are not up or down, but sideways Those parabolas have x=y squared, instead of y = x squared.
When the parabola concave downward and upward?
If the number in front of the x squared is negative, then the parabola will open upwards. The opposite occurs when the number is positive.
Is a parabola u shaped or n shaped if its x squared value is a negative fraction?
n shaped
Where is the vertex coordinate of the parabola y equals 24 -6x -3x squared when plotted on the Cartesian plane?
The vertex coordinate point of the vertex of the parabola y = 24-6x-3x^2 when plotted on the Cartesian plane is at (-1, 27) which can also be found by completing the square.
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.
How do you create an equation for a parabola?
An equation for a parabola always has some type of irregular variable, usually a squared variable or higher.
What is the shape of the graph of a quadratic function?
The graph of a quadratic function is a parabola. It can open either upward or downward depending on the sign of the coefficient of the squared term; if it is positive, the parabola opens upward, and if negative, it opens downward. The vertex of the parabola is its highest or lowest point, and the axis of symmetry is a vertical line that runs through this vertex.
What is Y equals x squared plus 1?
It is the equation of a parabola.
Parabola y equals one-fourth x squared?
Yes.
What is the coefficient of the squared expression in the parabolas equation?
The coefficient of the squared term in a parabola's equation, typically expressed in the standard form (y = ax^2 + bx + c), is represented by the value (a). This coefficient determines the direction and the width of the parabola: if (a > 0), the parabola opens upwards, and if (a < 0), it opens downwards. The larger the absolute value of (a), the narrower the parabola.
