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How do you solve a quadratic function when given the axis of symmetry and two points?
When you have the equation y-k=a(x-h)^2. You know the vertex=(h,k) And the axis of symmetry goes through the vertex; so h=the axis of symmetry. Say you have the axis is x=5. Thus h=5. Now all you have to do is plug in the two points in the eqaution and use a solution (try substitution) to solve for a. Then plug it back in to get k.
EX: x=5 (6,1) and (7,4)
1-k=a(6-5)^2 and 4-k=a(7-5)^2
1-k=a 4-k=4a
1-a=k *now substitute* 4-(1-a)=4a
4-1+a=4a
3=3a
a=1 (go back and plug in a)
k=1-1
k=0
The answer is: y=(x-5)
What else can I help you with?
What is the axis of symmetry of the quadratic function y 2(x 3)2 5?
The given quadratic function can be rewritten in standard form as ( y = 2(x - 3)^2 + 5 ). The axis of symmetry for a quadratic function in the form ( y = a(x - h)^2 + k ) is given by the line ( x = h ). Here, ( h = 3 ), so the axis of symmetry is ( x = 3 ).
What is the formula used to find the axis of symmetry?
The formula to find the axis of symmetry for a quadratic function in the form (y = ax^2 + bx + c) is given by (x = -\frac{b}{2a}). This vertical line divides the parabola into two mirror-image halves. The axis of symmetry passes through the vertex of the parabola and is crucial for graphing the function.
How do you Fit a quadratic function to these three points ( and minus1 and minus11) (0 and minus3) and (3 and minus27) y and minus4x2 and minus 4x and minus 3 y and minus4x2 plus 4x and minus 3 y and?
To fit a quadratic function to the points (-1, -11), (0, -3), and (3, -27), you can use the general form of a quadratic equation ( y = ax^2 + bx + c ). By substituting each point into the equation, you will create a system of three equations with three unknowns (a, b, and c). Solving this system will yield the coefficients that define the quadratic function that passes through the given points. In this case, the resulting quadratic function is ( y = -4x^2 - 4x - 3 ).
Does the formula for the area of the square with the side represent a quadratic function?
Yes, the formula for the area of a square, given by ( A = s^2 ) (where ( s ) is the length of a side), represents a quadratic function. The relationship between the area and the side length is quadratic because the highest exponent of the variable ( s ) is 2. This means that as the side length increases, the area increases at an increasing rate, characteristic of a quadratic function.
How do you know if a quadratic equation will have one two or no solutions How do you find a quadratic equation if you are only given the solution Is it possible to have different quadratic equation?
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
What is the axis of symmetry of the quadratic function y 2(x 3)2 5?
The given quadratic function can be rewritten in standard form as ( y = 2(x - 3)^2 + 5 ). The axis of symmetry for a quadratic function in the form ( y = a(x - h)^2 + k ) is given by the line ( x = h ). Here, ( h = 3 ), so the axis of symmetry is ( x = 3 ).
What name is given to the shape of a quadratic function?
A parabola
What is the formula used to find the axis of symmetry?
The formula to find the axis of symmetry for a quadratic function in the form (y = ax^2 + bx + c) is given by (x = -\frac{b}{2a}). This vertical line divides the parabola into two mirror-image halves. The axis of symmetry passes through the vertex of the parabola and is crucial for graphing the function.
How do you Fit a quadratic function to these three points ( and minus1 and minus11) (0 and minus3) and (3 and minus27) y and minus4x2 and minus 4x and minus 3 y and minus4x2 plus 4x and minus 3 y and?
To fit a quadratic function to the points (-1, -11), (0, -3), and (3, -27), you can use the general form of a quadratic equation ( y = ax^2 + bx + c ). By substituting each point into the equation, you will create a system of three equations with three unknowns (a, b, and c). Solving this system will yield the coefficients that define the quadratic function that passes through the given points. In this case, the resulting quadratic function is ( y = -4x^2 - 4x - 3 ).
How do you find the zeros of any given polynomial function?
by synthetic division and quadratic equation
What name is given to the turning point also known as the maximum or minimum of the graph of a quadratic function?
vertex
Does the formula for the area of the square with the side represent a quadratic function?
Yes, the formula for the area of a square, given by ( A = s^2 ) (where ( s ) is the length of a side), represents a quadratic function. The relationship between the area and the side length is quadratic because the highest exponent of the variable ( s ) is 2. This means that as the side length increases, the area increases at an increasing rate, characteristic of a quadratic function.
How do you know if a quadratic equation will have one two or no solutions How do you find a quadratic equation if you are only given the solution Is it possible to have different quadratic equation?
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
When do you say that the equation is a function or not?
i may only be 10 yrs old but i can say that an equation is not an function like the graphs of quadratic functions you will only be given an equation
Is it OK to use the quadratic formula if the given quadratic trinomial is not factorable?
Well, if the given quadratic equation cannot be factored, nor completed by the square, try using the quadratic formula.
Why isn't any other shapes beside a circle have infinitie symmetry lines?
only spheres take up all the given points in a given space
How do you calculate the profit maximizing output level given a total revenue and total cost function?
how to calculate profit maximizing water level under quadratic cost function
