Question 447907: for the quadratic function, write the equation of the axis of symmetry, and find the coordinates of the vertex
1)y=x^2+2x-9
2)y=1/2x^2-4x+3
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y=x^2+2x-9
To create a trinomial A polynomial consisting of three terms. Square a quadrilateral with four equal sides and four 90° angles. on the left-hand side of the equation A mathematical statement that says two expressions have the same value; any number sentence with an = . , add a value to both sides of the equation A mathematical statement that says two expressions have the same value; any number sentence with an = . that is equal to the square A quadrilateral with four equal sides and four 90° angles. of half either of the two quantities or pieces created when something is divided into two equal pieces. The coefficient A constant that multiplies a variable. Of "x." In this problem, add (1)^2 to both sides of the equation a mathematical statement that says two expressions have the same value; any number sentence with an = . .
y=x^2+2x+1-9
Factor one of two or more expressions that are multiplied together to get a product. The perfect trinomial a polynomial consisting of three terms. Square a quadrilateral with four equal sides and four 90° angles. Into (x+1)^2
y=(x+1)^2-9
Factor one of two or more expressions that are multiplied together to get a product. The perfect trinomial a polynomial consisting of three terms. . Square a quadrilateral with four equal sides and four 90° angles. Into (x+1)^2
y=(x+1)^2-9-1
Subtract 1 from -9 to get -10.
y=(x+1)^2-10
This is the form of a parabola. Use this form to determine the values used to find vertex The point on an angle where the two sides intersect, and x-y intercepts the x-intercept of a line or curve is the point where it crosses the x-axis, and the y-intercept of a line or curve is the point where it crosses the y-axis. .
y=a(x-h)^2+k
Use the standard form to determine the vertex the point on an angle where the two sides intersect. and x-y intercepts the x-intercept of a line or curve is the point where it crosses the x-axis, and the y-intercept of a line or curve is the point where it crosses the y-axis. .
a=1
k=-10
h=-1
The vertex the point on an angle where the two sides intersect. of a parabola set of points equally distant from a focus and a directrix. is (h,k).
Vertex the point on an angle where the two sides intersect. : (-1,-10)
This formula an equation that states a rule or a fact. is used to find the distance. Length, as between two points. from the vertex the point on an angle where the two sides intersect. to the focus imaginary point used in parabolas, hyperbolas, and ellipses. .
(1)/(4p)= a
Substitute the value of a into the formula an equation that states a rule or a fact. .
(1)/(4p)= 1
Solve the equation a mathematical statement that says two expressions have the same value; any number sentence with an = . for p.
p = (1)/(4)
Add p to the vertex the point on an angle where the two sides intersect. to find the focus imaginary point used in parabolas, hyperbolas, and ellipses. . If the parabola set of points equally distant from a focus and a directrix. points a location in a plane or in space, having no dimensions. up or down add p to the y-coordinate of the vertex the point on an angle where the two sides intersect. , if it points a location in a plane or in space, having no dimensions. left or right add it to the x-coordinate.
Focus= (-1, -10 + (1)/(4))
Find the focus imaginary point used in parabolas, hyperbolas, and ellipses. .
Focus = (-1, - (39)/(4))
A parabola set of points equally distant from a focus and a directrix. can also be defined as locus of points a location in a plane or in space, having no dimensions. in a plane a flat surface that stretches into infinity. which are equidistant the same distance. from a given point a location in a plane or in space, having no dimensions. (the focus) and a given line (the directrix) a fixed line associated with a parabola. .
y= (-10)-(1)/(4)
Find the directrix a fixed line associated with a parabola. .
Directrix a fixed line associated with a parabola. : y= - (41)/(4)
The axis the horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is usually called the x-axis, the vertical axis is usually called the y-axis. of symmetry a correspondence of parts. is the line that passes through the vertex the point on an angle where the two sides intersect. and focus imaginary point used in parabolas, hyperbolas, and ellipses. . The two sides of a graph avisual representation of data. on either side of the axis the horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is usually called the x-axis, the vertical axis is usually called the y-axis. of symmetry a correspondence of parts. look like mirror images the result of a transformation on an object. of each other.
Axis the horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is usually called the x-axis, the vertical axis is usually called the y-axis. of Symmetry a correspondence of parts. : x=-1
These values represent the important values for graphing and analyzing a parabola set of points equally distant from a focus and a directrix. .
Vertex the point on an angle where the two sides intersect. : (-1,-10)
Focus imaginary point used in parabolas, hyperbolas, and ellipses. :
(-1, - (39)/(4))
Directrix a fixed line associated with a parabola. : y= -(41)/(4)
Axis the horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is usually called the x-axis; the vertical axis is usually called the y-axis. of
Symmetry a correspondence of parts. :
Vertex: (-1,-10)
Focus: (-1, - (39)/(4))
Directrix: y= - (41)/(4)
Axis of Symmetry: x=-1
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y=1/2x^2-4x+3
Multiply to compute a product; to perform a multiplication. (1)/(2)by x^2 to get (x^2)/(2)
y=x^2/2-4x+3
To create a trinomial a polynomial consisting of three terms. square a quadrilateral with four equal sides and four 90° angles. on the left-hand side of the equation a mathematical statement that says two expressions have the same value; any number sentence with an = . , add a value to both sides of the equation a athematical statement that says two expressions have the same value; any number sentence with an = . that is equal to the square a quadrilateral with four equal sides and four 90° angles. of half either of the two quantities or pieces created when something is divided into two equal pieces. the coefficient a constant that multiplies a variable. of x. In this problem, add (-4)^2 to both sides of the equation a mathematical statement that says two expressions have the same value; any number sentence with an = . .
y=〖1((x) 〗^2-8x+16)/2+(1)(16)/(2/(2/2))
Factor one of two or more expressions that are multiplied together to get a product. the perfect trinomial a polynomial consisting of three terms. Square a quadrilateral with four equal sides and four 90° angles. Into (x-4)^2
y=〖1(x-4)〗^2/2+(1)(16)/(2/(2/2))
Factor one of two or more expressions that are multiplied together to get a product. the perfect trinomial a polynomial consisting of three terms. Square a quadrilateral with four equal sides and four 90° angles. into (x*-4)^2
y=〖1(x-4)〗^2/2+ 1(6)-(1)(16)/2
This is the form of a parabola. Use this form to determine the values used to find vertex the point on an angle where the two sides intersect. and x-y intercepts the x-intercept of a line or curve is the point where it crosses the x-axis, and the y-intercept of a line or curve is the point where it crosses the y-axis. .
y=a(x-h)^2+k
Use the standard form to determine the vertex the point on an angle where the two sides intersect. and x-y intercepts the x-intercept of a line or curve is the point where it crosses the x-axis, and the y-intercept of a line or curve is the point where it crosses the y-axis. .
a=(1)/(2)
k=1(6)
h=4
The vertex of a parabola s (h,k).
Vertex: (4,1(6))
(1)/(4p)= a
Substitute the value of "a" into the formula .
(1)/(4p)= (1)/(2)
Solve the equation a mathematical statement that says two expressions have the same value; any number sentence with an = . for p.
p = (1)/(2)
Add p to the vertex the point on an angle where the two sides intersect. to find the focus imaginary point used in parabolas, hyperbolas, and ellipses. . If the parabola set of points equally distant from a focus and a directrix. points a location in a plane or in space, having no dimensions. up or down add p to the y-coordinate of the vertex the point on an angle where the two sides intersect. , if it points a location in a plane or in space, having no dimensions. left or right add it to the x-coordinate.
Focus = (4, 1(6) +(1)/(2))
Find the focus imaginary point used in parabolas, hyperbolas, and ellipses. .
Focus = (4, (13)/(2))
y= 1(6) - ((1)/(2))
Directrix : y= (11)/(2)
Vertex the point on an angle where the two sides intersect. : (4,1(6))
Focus imaginary point used in parabolas, hyperbolas, and ellipses. : (4, (13)/(2))
Directrix a fixed line associated with a parabola. : y= (11)/(2)
Axis the horizontal and vertical lines that form the quadrants of the coordinate plane. The horizontal axis is usually called the x-axis, the vertical axis is usually called the y-axis. of
Symmetry a correspondence of parts. :
Axuis of Symmetry : x=4
Focus : (4, (13)/(2))
Directrix : y= (11)/(2)
Vertex : (4,1(6))
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