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Wize High School Grade 10 Math Textbook > Vertex Form of a Quadratic Equation

Determining the Quadratic Equation in Vertex Form

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Example: Deterining the Equation of a Quadratic Graph

Determine the equation of the following graph in vertex form y=a(x−h)2+ky=a\left(x-h\right)^2+k


  • The vertex is (−3, −1)\left(-3,\ -1\right), so h=−3, k=−1\boxed{h=-3},\ \boxed{k=-1}
  • The parabola opens down, so aa is negative
  • It appears that there is a vertical stretch. From the vertex (−3, −1)\left(-3,\ -1\right), we have to "walk" 1 unit to the right, and 2 units down to get to another point on the graph. So, a=−2\boxed{a=-2}
So, the equation of the graph is y=−2(x+3)2−1y=-2(x+3)^2-1

Practice: Determining the Equation of a Quadratic Graph

Determine the equation of the graph that is obtained by applying the following transformations to the graph y=x2y=x^2.

i) A horizontal shift 44 units to the left.
ii) A vertical compression by a factor of 13\dfrac{1}{3}.
iii) A vertical reflection along the x-axis.
iv) A vertical shift 22 units down.

Practice: Determining the Equation of a Quadratic Graph

Write the equation of the following graph.


Practice: Determining the Equation of a Quadratic Graph

Express y=−2(x−1)(x−3)y=-2\left(x-1\right)\left(x-3\right) in vertex form y=a(x−h)2+ky=a\left(x-h\right)^2+k

Practice: Determining the Equation of a Quadratic Graph

What is the equation of the graph that has a vertex at (1,3)(1,3) and has a y-intercept at y=5y=5.