Mathematics
Grade10
Easy

Question

Find the solutions for the equation y equals x squared plus 4 x minus 6 using vertex form.

  1. 2 plus-or-minus square root of 10
  2. negative 1 plus-or-minus square root of 10
  3. negative 2 plus-or-minus square root of 10
  4. 1 plus-or-minus square root of 10

hintHint:

In this question, we have to find the solutions for the equation y equals x squared plus 4 x minus 6 using vertex form. Vertex form is another form of a quadratic equation. The standard form of a quadratic equation is ax squared + bx + c. The vertex form of a quadratic equation is a left parenthesis x minus h right parenthesis squared + k where a is a constant that tells us whether the parabola opens upwards or downwards, and (h, k) is the location of the vertex of the parabola. 

The correct answer is: negative 2 plus-or-minus square root of 10


    Given quadratic equation, y equals x squared plus 4 x minus 6
    Now we isolate constants to the other side,
    y plus 6 equals x squared plus 4 x
    Adding 4 on both sides, we get
    y plus 6 plus 4 equals x squared plus 4 x plus 4
y plus 10 equals left parenthesis x plus 2 right parenthesis squared
y equals left parenthesis x plus 2 right parenthesis squared minus 10
    The vertex form of the quadratic equation is y equals left parenthesis x plus 2 right parenthesis squared minus 10.
    Solutions are equals negative 2 plus-or-minus square root of 10

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