Vertex/Axis of Symmetry for x^2+2x=35

May 2024 · 3 minute read
Vertex/Axis of Symmetry for x^2+2x=35

Vertex/Axis of Symmetry for x^2+2x=35

Image to Crop Find the vertex, vertex form, and axis of symmetry for
x^2+2x=35

The quadratic you entered is not in standard form: ax2 + bx + c = 0

Subtract 35 from both sides

x2+2x - 35 = 35 - 35
x2+2x - 35 = 0

We have our a, b, and c values:
a = 1, b = 2, c = -35

Find the vertex, vertex form, and axis of symmetry of the quadratic
x2 + 2x - 35=

Vertex of a parabola

(h,k) where y = a(x - h)2 + kUse the formula rule.

Our equation coefficients are a = 1, b = 2

The formula rule determines h

h = Axis of Symmetry
h  =  -b
  2a

Plug in -b = -2 and a = 1

h  =  -(2)
  2(1)

h  =  -2
  2

h = -1  ← Axis of Symmetry

Calculate k

k = ƒ(h) where h = -1
ƒ(h) = (h)2(h)35=
ƒ(-1) = (-1)2(-1)35=
ƒ(-1) = 1 - 2 - 35
ƒ(-1) = -36
Our vertex (h,k) = (-1,-36)

Determine our vertex form:

The vertex form is: a(x - h)2 + k
Vertex form = (x + 1)2 - 36

h = -1
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36


What is the Answer?

h = -1
vertex (h,k) = (-1,-36)
Vertex form = (x + 1)2 - 36

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

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