Questions: Non-Linear Relation complete y-intercept and these parabola the equations for 1 y=2 x^2+□ y=-1 / 2 x^2+ □

Non-Linear Relation complete y-intercept and these parabola the equations for 1 y=2 x^2+□ y=-1 / 2 x^2+ □
Transcript text: Non-Linear Relation complete $y$-intercept and these parabol the equations for 1 \[ y=2 x^{2}+\square \] $y=-1 / 2 x^{2}+$ $\square$
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Solution

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Solution Steps

Step 1: Identify the y-intercept for each parabola
  • For the first parabola, the y-intercept is 5.
  • For the second parabola, the y-intercept is 2.
  • For the third parabola, the y-intercept is 1.
Step 2: Write the general form of the quadratic equation
  • The general form of a quadratic equation is \( y = ax^2 + c \), where \( c \) is the y-intercept.
Step 3: Substitute the y-intercept into the equation
  • For the first parabola: \( y = 2x^2 + 5 \)
  • For the second parabola: \( y = -\frac{1}{2}x^2 + 2 \)
  • For the third parabola: \( y = x^2 + 1 \)

Final Answer

  1. \( y = 2x^2 + 5 \)
  2. \( y = -\frac{1}{2}x^2 + 2 \)
  3. \( y = x^2 + 1 \)
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