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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.
How do you rewrite the equation of a parabola in standard form?
To rewrite the equation of a parabola in standard form, you need to express it as ( y = a(x - h)^2 + k ) for a vertically oriented parabola or ( x = a(y - k)^2 + h ) for a horizontally oriented parabola. Here, ( (h, k) ) represents the vertex of the parabola, and ( a ) determines its direction and width. You can achieve this by completing the square on the quadratic expression.
How does the value a affect the width of the parabola?
In a quadratic equation of the form (y = ax^2 + bx + c), the value of (a) determines the width of the parabola. If (|a|) is greater than 1, the parabola is narrower, indicating that it opens more steeply. Conversely, if (|a|) is less than 1, the parabola is wider, meaning it opens more gently. The sign of (a) also affects the direction of the opening: positive values open upwards, while negative values open downwards.
How the value of a in the standard form of a equadratic affects the direction and shape of the graph?
In the standard form of a quadratic equation ( y = ax^2 + bx + c ), the value of ( a ) determines the direction and the shape of the graph. If ( a > 0 ), the parabola opens upwards, while if ( a < 0 ), it opens downwards. Additionally, the absolute value of ( a ) affects the width of the parabola: larger values of ( |a| ) result in a narrower graph, while smaller values lead to a wider graph.
What could be the equation of a parabola with its vertex at (-36).?
The equation of a parabola with its vertex at the point (-36, k) can be expressed in the vertex form as ( y = a(x + 36)^2 + k ), where ( a ) determines the direction and width of the parabola. If the vertex is at (-36), the x-coordinate is fixed, but the y-coordinate ( k ) can vary depending on the specific position of the vertex. If you'd like a specific example, assuming ( k = 0 ) and ( a = 1 ), the equation would be ( y = (x + 36)^2 ).
How do you find the length and width of a rectangle when given the area and perimeter?
By forming a quadratic equation from the information given and then the length and width can be found by solving the equation.
What does 14mm mean for a watch band?
MM is millimeter. Determines the width of the piece. The watch band is 14mm in width.
What determines the size of a belt sander?
The width of the rollers and distance they are apart.
What determines the size of an object?
Three dimensions: Height Width Length
What is the quadratic equation and area of a rectangle when its length is 7 cm greater than its width which is 3x cm?
Quadratic equation: 9x2-21x+12.25 = 0 Area: 36.75 square cm
What determines the size of a portable belt sander?
The width of the rollers and distance they are apart.
What determines the amount of data that can be sent at one time?
bus width
What is the equation Area length X width used for?
the equations tell you what the surface area of somthing is
The Perimeter of a rectangle is 56cm The length is 2cm less than twice the width find the length and width?
length=18cm width=10cm (you use a system of equations: 2L+2W=56, L=2W-2)
Can autofit determines the best width for a column or the best height for a row based on its contents?
yes
What is a real life example of factoring quadratic equations with solution?
Example:- What are the dimensions of a rectangle when its length is greater than its width by 4 cm and has an area of 96 square cm? Let the length be x+4 and the width x: length*width = area (x+4)*x = 96 => x2+4x-96 = 0 => (x+12)(x-8) = 0 when factored So: x = -12 or x = 8 the dimensions can't be negative Solution: length = 12 cm and width = 8 cm Check: 12*8 = 96 square cm
Determines the best width for a colume or the best height for a row based on its contents?
Everyone reading this is gay!
