how do you solve a quadratic equation in vertex form?
14192
To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex. Equation in y = ax2 + bx + c form.
239722
['Use the graph of y = x2 + x - 6 to solve x2 + x - 6 = 0.', 'Use the graph of y = -x2 + 4 to solve -x2 + 4 = 0.', 'Use the graph of y = x2 -2x + 1 to solve x2 -2x + 1.']
65498
['Check the Equation.', 'Press Mode, then 1.', 'Select the Quadratic Equation.', 'Input Your Values.']
173213
If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: (y - k)2 = 4p(x - h), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p.
280954
We can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property. The Zero Product Property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.
61439
['Quadratic Equation in Standard Form: ax2 + bx + c = 0.', 'Quadratic Equations can be factored.', 'Quadratic Formula: x = −b ± √(b2 − 4ac) 2a.', 'When the Discriminant (b2−4ac) is: positive, there are 2 real solutions. zero, there is one real solution. negative, there are 2 complex solutions.']
1315032
['Solution.', 'Step 1: Add or subtract the constant term to obtain an equation of the form x2+bx=c. ... ', 'Step 2: Use (b2)2 to determint the value that completes the square. ... ', 'Step 3: Add (b2)2 to both sides of the equation and complete the square.', 'Step 4: Solve by extracting roots.', 'Answer:']
844849
Thus, if a quadratic has two real roots α,β, then the x-coordinate of the vertex is 12(α+β). ... Thus we can express the sum of the roots in terms of the coefficients a,b,c of the quadratic as α+β=−ba.
134635
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
180872
The vertex form of a quadratic is given by. y = a(x – h)2 + k, where (h, k) is the vertex. The "a" in the vertex form is the same "a" as. in y = ax2 + bx + c (that is, both a's have exactly the same value). The sign on "a" tells you whether the quadratic opens up or opens down.
929696
The standard form of a quadratic equation in one variable is ax^2 + bx + c = 0.
995769
The standard form of an equation of a hyperbola centered at the origin with vertices (±a,0) ( ± a , 0 ) and co-vertices (0±b) ( 0 ± b ) is x2a2−y2b2=1 x 2 a 2 − y 2 b 2 = 1 .
227403
['Use the graph of y = x2 + x - 6 to solve x2 + x - 6 = 0.', 'Use the graph of y = -x2 + 4 to solve -x2 + 4 = 0.', 'Use the graph of y = x2 -2x + 1 to solve x2 -2x + 1.', 'Use the graph of y = x2 + 1 to solve x2 + 1.']
702018
Don't be fooled: Not all quadratic equations can be solved by factoring. For example, x2 - 3x = 3 is not solvable with this method. One way to solve quadratic equations is by completing the square; still another method is to graph the solution (a quadratic graph forms a parabola—a U-shaped line seen on the graph).
845204
Examples of Quadratic Equation. A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
177028
['Get the equation in the form y = ax2 + bx + c.', 'Calculate -b / 2a. This is the x-coordinate of the vertex.', 'To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.']
1182674
Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.