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The expression ( y = ax - h + k ) represents a linear equation in slope-intercept form, where ( a ) is the slope, ( -h ) is a horizontal shift, and ( k ) is a vertical shift. The term ( h ) adjusts the x-coordinate of the graph, moving it left or right, while ( k ) adjusts the y-coordinate, moving it up or down. Overall, this equation describes how a line can be transformed from its standard position based on shifts and slope.
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How do you change vertex form to standard form?
To convert a quadratic equation from vertex form ( y = a(x - h)^2 + k ) to standard form ( y = ax^2 + bx + c ), you need to expand the squared term. First, expand ( (x - h)^2 ) to get ( x^2 - 2hx + h^2 ). Then, multiply this by ( a ) and add ( k ), resulting in ( y = ax^2 - 2ahx + (ah^2 + k) ), which gives you the coefficients for ( ax^2 + bx + c ).
How do you convert vertex form to standard form in algebra?
To convert a quadratic equation from vertex form, (y = a(x - h)^2 + k), to standard form, (y = ax^2 + bx + c), you need to expand the equation. Start by squaring the binomial: ( (x - h)^2 = x^2 - 2hx + h^2 ). Then, multiply by (a) and add (k) to obtain (y = ax^2 - 2ahx + (ah^2 + k)), where (b = -2ah) and (c = ah^2 + k). This results in the standard form of the quadratic equation.
Write the equation of the line in the form Ax plus By equals C?
Ax + By = C By = -Ax + C y = (-A/B)x + C/B
How do you convert a vertex form equation of a parabola 2 standard form equation?
To convert a vertex form equation of a parabola, given as ( y = a(x - h)^2 + k ), to standard form ( y = ax^2 + bx + c ), expand the squared term: ( (x - h)^2 = x^2 - 2hx + h^2 ). Then, multiply through by ( a ) and combine like terms: ( y = ax^2 - 2ahx + (ah^2 + k) ). The coefficients ( a ), ( b = -2ah ), and ( c = ah^2 + k ) represent the standard form parameters.
The vertex form of the equation of a parabola is . What is the standard form of the equation?
To convert the vertex form of a parabola, which is typically expressed as (y = a(x-h)^2 + k), into standard form (y = ax^2 + bx + c), you need to expand the equation. Start by squaring the binomial ((x-h)), which gives (x^2 - 2hx + h^2). Then, distribute the coefficient (a) and combine like terms to achieve the standard form. The resulting equation will be (y = ax^2 - 2ahx + (ah^2 + k)).
How do you change vertex form to standard form?
To convert a quadratic equation from vertex form ( y = a(x - h)^2 + k ) to standard form ( y = ax^2 + bx + c ), you need to expand the squared term. First, expand ( (x - h)^2 ) to get ( x^2 - 2hx + h^2 ). Then, multiply this by ( a ) and add ( k ), resulting in ( y = ax^2 - 2ahx + (ah^2 + k) ), which gives you the coefficients for ( ax^2 + bx + c ).
What is factor ax plus ay plus AZ?
a(x + y + z)
How do you convert vertex form to standard form in algebra?
To convert a quadratic equation from vertex form, (y = a(x - h)^2 + k), to standard form, (y = ax^2 + bx + c), you need to expand the equation. Start by squaring the binomial: ( (x - h)^2 = x^2 - 2hx + h^2 ). Then, multiply by (a) and add (k) to obtain (y = ax^2 - 2ahx + (ah^2 + k)), where (b = -2ah) and (c = ah^2 + k). This results in the standard form of the quadratic equation.
Write the equation of the line in the form Ax plus By equals C?
Ax + By = C By = -Ax + C y = (-A/B)x + C/B
How do you convert a vertex form equation of a parabola 2 standard form equation?
To convert a vertex form equation of a parabola, given as ( y = a(x - h)^2 + k ), to standard form ( y = ax^2 + bx + c ), expand the squared term: ( (x - h)^2 = x^2 - 2hx + h^2 ). Then, multiply through by ( a ) and combine like terms: ( y = ax^2 - 2ahx + (ah^2 + k) ). The coefficients ( a ), ( b = -2ah ), and ( c = ah^2 + k ) represent the standard form parameters.
The vertex form of the equation of a parabola is . What is the standard form of the equation?
To convert the vertex form of a parabola, which is typically expressed as (y = a(x-h)^2 + k), into standard form (y = ax^2 + bx + c), you need to expand the equation. Start by squaring the binomial ((x-h)), which gives (x^2 - 2hx + h^2). Then, distribute the coefficient (a) and combine like terms to achieve the standard form. The resulting equation will be (y = ax^2 - 2ahx + (ah^2 + k)).
What kind of equation is y equals ax plus b?
a function
Factor the following expression ax plus ay minus AZ?
ax + ay - AZ = a(x + y - z)
Explain how to determine the y-intercept of the line whose equation is Ax plus By equals C?
Ax + By = CSubtract 'Ax' from each side:By = -Ax + CDivide each side by 'B' :y = -(A/B)x + C/BThe slope of the line is -(A/B) .The y-intercept is (C/B) .
Put the equation y minus 8 equals x squared plus 12 x plus 36 in vertex form f left paren x right paren equals a left paren x minus h right paren squared plus k and find values for a h and k?
y - 8 = x^2 + 12x + 36 y - 8 = (x + 6)^2 y = (x + 6)^2 + 8 or f(x) = (x + 6)^2 + 8 So -h = 6 so that h = -6, and k = 8
How do you solve the B in Ax plus By equals C?
To solve for B in the equation ( Ax + By = C ), you first isolate the term involving B. Rearranging gives ( By = C - Ax ). Then, divide both sides by y (assuming y is not zero) to solve for B: ( B = \frac{C - Ax}{y} ).
How is the vertex form of an equation different from the standard form and what values change the shape of the graph?
The vertex form of a quadratic equation is expressed as ( y = a(x-h)^2 + k ), where ((h, k)) is the vertex of the parabola, while the standard form is ( y = ax^2 + bx + c ). In vertex form, the values of (a), (h), and (k) directly influence the shape and position of the graph; specifically, (a) determines the width and direction of the parabola, while (h) shifts it horizontally and (k) shifts it vertically. Changes to (a) affect the steepness, while altering (h) and (k) moves the vertex without changing the graph's shape.
