3-1 Key Features of Parabolas

What is the axis of symmetry in a parabola?

• A vertical line that divides the parabola into two mirror-image halves and passes through the vertex.

• A horizontal line that divides the parabola into two equal parts.

• A diagonal line that intersects the parabola at two points.

• A curved line that follows the shape of the parabola.

How do you find the maximum or minimum value of a parabola?

• At the x-intercepts of the parabola.

• At the vertex of the parabola. The y-coordinate of the vertex gives this value.

• By calculating the roots of the equation.

• By using the quadratic formula to find the values.

What is the effect of changing the value of 'c' in the quadratic equation?

• It shifts the parabola left or right along the x-axis.

• It changes the shape of the parabola, making it wider or narrower.

• It shifts the parabola up or down along the y-axis, affecting the y-intercept.

• It reflects the parabola across the x-axis.

What is the vertex of a parabola?

• The point where the parabola changes direction.

• The point where the parabola intersects the x-axis.

• The point where the parabola intersects the y-axis.

• The point where the parabola is widest.

What is the significance of the coefficient 'a' in a quadratic equation?

• It determines the roots of the equation.

• It affects the linearity of the equation.

• It determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

• It indicates the maximum value of the quadratic function.

What is the standard form of a quadratic equation?

• y = ax² + bx + c, where a, b, and c are constants.

• y = a(x - h)² + k, where (h, k) is the vertex.

• y = mx + b, where m is the slope and b is the y-intercept.

• y = a(x + p)(x + q), where p and q are the roots.

How can you determine the number of x-intercepts a parabola has?

• By finding the vertex of the parabola

• By using the discriminant (b² - 4ac) of the quadratic equation

• By calculating the slope of the parabola

• By determining the axis of symmetry

What is the effect of changing the value of 'b' in the quadratic equation?

• It affects the position of the vertex along the x-axis and can change the axis of symmetry.

• It changes the value of the discriminant only.

• It determines the direction of the parabola's opening.

• It has no effect on the graph of the equation.

How do you graph a parabola?

• Identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them.

• Draw a straight line through the vertex and intercepts.

• Use a ruler to connect the vertex to the intercepts.

• Plot random points on the graph and connect them.

How do you find the y-intercept of a parabola?

• By evaluating the quadratic equation at x = 0.

• By finding the vertex of the parabola.

• By calculating the roots of the equation.

• By determining the maximum value of the parabola.