algebra

• The coefficient of x^2 is -3
• To find the value of an expression when x = 4, substitute 4 into the expression.
• The constant term is 10
• When finding the value of an expression with variables raised to powers, use the power rule (a^m * a^n = a^(m+n)).
• The discriminant of a quadratic equation determines whether it has real or complex roots.
• If there are no terms containing x, then the equation simplifies to y=5x-7.
• A quadratic equation has two solutions (roots) which are real or complex numbers.
• A quadratic function can be written as f(x) = ax^2 + bx + c.
• If the discriminant is negative, there are no real solutions.
• If the discriminant is zero, there is one repeated root.
• If the discriminant is positive, there are two distinct real solutions.
• The quadratic formula can be used to solve any quadratic equation in standard form.
• Simplify the expression by combining like terms.
• If the discriminant is negative, there are no real roots.
• The equation of the line tangent to the curve at the point (h, k) is given by y - k = m(x - h), where m is the slope of the tangent line.
• The vertex form of a parabola is given by f(x) = a(x - h)^2 + k.
• To find the vertex of a parabola, set the expression inside the square brackets equal to zero and solve for x.
• The equation of the line tangent to the graph at the point (h, k) is given by y - k = m(x - h), where m is the slope of the tangent line.
• To find the vertex of a parabola, set the derivative equal to zero and solve for x.
• The standard form of a quadratic equation is Ax^2 + Bx + C = 0.
• The equation of the perpendicular bisector of the chord joining points A(-3, 4) and B(5, 6) is given by y - 4 = (-8)(x - 0)/9.
• The equation of the perpendicular bisector of the chord joining points A(-3, 4) and B(5, 6) is given by y - 4 = (-8)(x - 0)/9.
• The standard form of an ellipse with center at the origin is given by (x^2/a^2) + (y^2/b^2) = 1.
• The equation of the normal line to the graph at the point (h, k) is given by y - k = -1/m(x - h).
• The focus of a parabola lies on its axis of symmetry.
• The quadratic formula is derived from completing the square.
• To find the x-intercepts of a quadratic function, set it equal to zero and solve for x.
• A quadratic equation has two possible forms: vertex form or factored form.
• To find the coordinates of the vertex of a parabola, substitute the value of m into the expression for the equation of the tangent at any point P(x, y), then solve for x.
• To find the roots of a quadratic equation, set the discriminant equal to zero.
• A circle can be represented parametrically as x = r cos t and y = r sin t.
• The equation of the tangent line to the curve f(x) = x^2 - 2x + 7 at the point where x = 2 is given by y - 13 = -2(x - 2).
• The equation of the normal line to the curve y = e^x at the point P(x_1, y_1) is given by y - y_1 = -1/(e^{x_1}) * (x - x_1).
• The equation of the axis of symmetry of the parabola y = x^2 - 7x + 10 is given by x = 7/2.
• The equation of the normal to the curve y = x^2 - 1 at the point P(2, 3) is given by y - 3 = -2/3(x - 2).
• The quadratic formula is useful when finding the roots of a quadratic equation without using a graphing calculator.
• The quadratic formula can be used to find the roots of any quadratic equation.
• The discriminant of a quadratic function determines whether there are real solutions.
• The discriminant of a quadratic function determines whether there are real solutions.
• If two lines are parallel or coincident, their slopes are equal.