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You must first solve the equation for x, find the midpoint between the two x coordinates and substitute it into the equation to find the y coordinate
I.E.
If your equation was y=x^2+4x-5
1. Factorise the Equation and solve for x. x^2+4x-5 = (x+5)(x-1)
So x+5=0
x = 0 - 5
x=-5
And x-1=0
x = 0 + 1
x = 1
So x = -5,1
Find the mid point/average: (-5+1)/2 = -2
So the x coordinate of the vertex is -2.
Substitute this into the equation x^2+4x-5: (-2)^2 + 4*(-2) - 5 = 4 - 8 - 5 = -9
So the Coordinate of the vertex is (-2,-9).
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What else can I help you with?
How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
What is the equation of vertex in parabola?
0,0
The vertex of the parabola below is at the point (5 -3). Which of the equations below could be the one for this parabolaus anything?
To determine the equation of a parabola with a vertex at the point (5, -3), we can use the vertex form of a parabola's equation: (y = a(x - h)^2 + k), where (h, k) is the vertex. Substituting in the vertex coordinates, we have (y = a(x - 5)^2 - 3). The value of "a" will determine the direction and width of the parabola, but any equation in this form with varying "a" values could represent the parabola.
What is the y-coordinate of the vertex of the parabola that is given by the equation below?
We will be able to identify the answer if we have the equation. We can only check on the coordinates from the given vertex.
Fill in the blank The of the vertex of a quadratic equation is determined by substituting the value of x from the axis of symmetry into the quadratic equation?
D
What is a quadratic equation in vertex form for a parabola with vertex (11 -6)?
A quadratic equation in vertex form is expressed as ( y = a(x - h)^2 + k ), where ((h, k)) is the vertex of the parabola. For a parabola with vertex at ((11, -6)), the equation becomes ( y = a(x - 11)^2 - 6 ). The value of (a) determines the direction and width of the parabola. Without additional information about the parabola's shape, (a) can be any non-zero constant.
What different information do you get from vertex form and quadratic equation in standard form?
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
What is the average of the two roots of quadratic equation?
In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.
What is the equation of vertex in parabola?
0,0
What is the highest or lowest point on the graph of a quadratic function?
The highest or lowest point on the graph of a quadratic function, known as the vertex, depends on the direction of the parabola. If the parabola opens upwards (the coefficient of the (x^2) term is positive), the vertex represents the lowest point. Conversely, if the parabola opens downwards (the coefficient is negative), the vertex is the highest point. The vertex can be found using the formula (x = -\frac{b}{2a}) to find the (x)-coordinate, where (a) and (b) are the coefficients from the quadratic equation (ax^2 + bx + c).
If the discriminant of an equation is zero then what is true about the equation?
If the discriminant of a quadratic equation is zero, it indicates that the equation has exactly one real solution, also known as a double root. This means the parabola represented by the quadratic touches the x-axis at a single point rather than crossing it. In other words, the vertex of the parabola lies on the x-axis.
The number of solution a quadratic equation has?
A quadratic equation always has 2 solutions.In the instance of perfect squares, however, there will be just one number, which is a double root. Graphically, this is equivalent of the vertex of a parabola just barely touching the x-axis.
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 vertex of a parabola that opens down called?
The vertex of a parabola that opens down is called the maximum point. This point represents the highest value of the function described by the parabola, as the graph decreases on either side of the vertex. In a quadratic equation of the form (y = ax^2 + bx + c) where (a < 0), the vertex can be found using the formula (x = -\frac{b}{2a}). The corresponding (y)-value can then be calculated to determine the vertex's coordinates.
When the coefficient of x2 is negative?
When the coefficient of ( x^2 ) is negative in a quadratic equation, the parabola opens downward. This means that the vertex of the parabola represents a maximum point, and the value of the function decreases on either side of the vertex. Consequently, the graph will touch or cross the x-axis at most twice, indicating that the quadratic can have zero, one, or two real roots.
