Quadratics

What is the y-intercept of a quadratic function?

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

• The point where the parabola crosses the y-axis, found by evaluating the function at @@x = 0@@.

• The maximum value of the quadratic function.

• The minimum value of the quadratic function.

What is the standard form of a quadratic equation?

• y = ax^2 + bx + c

• y = ax^2 - bx + c

• y = a + b + c

• y = ax^2 + b + c

What is the vertex of a parabola?

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

• The highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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

• The midpoint of the line segment connecting the focus and directrix.

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

• By evaluating the function at its endpoints

• By using the formula @@x = -\frac{b}{2a}@@ to find the vertex

• By taking the derivative and setting it to zero

• By completing the square

What does the 'a' value in the quadratic equation @@y = ax^2 + bx + c@@ determine?

• The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

• The 'a' value determines the width of the parabola: larger values make it wider, smaller values make it narrower.

• The 'a' value determines the vertex of the parabola: it sets the highest or lowest point.

• The 'a' value determines the x-intercepts of the parabola: it affects where the graph crosses the x-axis.

What is the significance of the discriminant in a quadratic equation?

• It determines the coefficients of the equation.

• It indicates the number of solutions: if D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

• It provides the vertex of the parabola.

• It calculates the area under the curve.

What is the vertex form of a quadratic equation?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

• y = a(x - h)^2 - k

What is the minimum value of the quadratic function @@y = 2x^2 - 8x + 6@@?

• -2

• 0

• 2

• 4

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.

If the vertex of a parabola is (h, k), what is the equation of the axis of symmetry?

• x = h

• y = k

• y = h

• x = k