QUADRATIC GRAPHS

• What type of equations do quadratic graphs represent?

  Quadratic equations
• Why are the equations quadratic?


  Because they all have an $x^2$ term
• What is the defining characteristic of quadratic graphs regarding the powers of x?


  They do not have any higher powers of x like $x^3$ or $x^4$
• What shape do quadratic graphs always have?


  A smooth curved shape
• What is always present in the middle of a quadratic graph?


  A line of symmetry
• What does a positive $x^2$ term indicate about the direction of the curve?


  The curve will face upwards
• What does a negative $x^2$ term indicate about the direction of the curve?


  The curve will face downwards
• What is the simplest quadratic graph equation?


  $y =$$x^2$
• Where does the graph of $y =$$x^2$ cross the axis?


  At the point (0, 0)
• How does the graph of $y =$$-x^2$ differ from $y =$$x^2$?


  It curves downwards instead of upwards
• What effect does changing the coefficient of $x^2$ have on the graph?


  It changes the width of the curve
• What happens to the graph when the equation is $y =$$2x^2$ compared to $y =$$x^2$?


  The curve becomes narrower
• What does the equation $y =$$2x^2 - 3$ do to the graph?


  It moves the curve downwards
• How does the equation $y =$$2x^2 - 5x - 3$ affect the graph's position?


  It moves the curve further down and to the right
• What are the key characteristics of quadratic graphs?


  • Represent quadratic equations
  • Have a smooth curved shape
  • Always have a line of symmetry
  • Positive $x^2$ term means upward curve
  • Negative $x^2$ term means downward curve
• How do changes in the quadratic equation affect the graph?


  • Changing coefficients alters the width of the curve
  • Adding or subtracting constants shifts the graph vertically
  • Changing linear terms shifts the graph horizontally